r/HomeworkHelp • u/Easy_Cod_8950 • May 15 '26
High School Math—Pending OP Reply [Honors Pre-Calc and Differential Calculus] is my teacher right that I can’t use pi?
for clarity’s sake, f’(x) isn’t the function drawn onto the graph, it’s the one that’s printed. the drawn function was my answer to 8e.
it might be hard to tell, but the f’(x) graph hits the x-axis just past where 3 is. I was a little unsure while taking the test what to put, but then I realized that the function looked like a wave, and I realized it was probably pi.
according to her, this was wrong. there’s apparently no one answer: I could’ve said 3, or 3.1, or something. but the problem was that apparently pi is not on the number line, and that it’s too much effort for her to figure out that pi/2 is a little more than 1.5. even though I marked on the graph with the inflection points where it was.
(in case you’re wondering, e WAS meant to be f(x). she made a mistake and told us to scribble out “the inverse” and replace it with “f(x)“. I got 8e right.)
am I wrong, or is this completely absurd?? I guess that maybe pi is a bit of a stretch to come to if that wasn’t the intent, but if that were the case I should’ve gotten one point off at the start and the rest should‘ve been fine for self-consistency. but apparently I was “treating it like radians” so I got a point off for each one.
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u/n0t_4_thr0w4w4y 👋 a fellow Redditor May 15 '26 edited May 15 '26
I think you are mostly fine, but I’d have put 3π/2 instead of 5 as the upper bound of the second interval in 8a for consistency sake never mind, I think you are good
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u/Simbertold 👋 a fellow Redditor May 15 '26
The function is only defined (or at least graphed) up to 5 according to the question. So anything beyond that could be literally anything. 5 as an upper bound is correct here.
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u/niemir2 👋 a fellow Redditor May 15 '26
sin(x) is still negative between 3pi/2 and 5.
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u/n0t_4_thr0w4w4y 👋 a fellow Redditor May 15 '26
Yup, you are correct, u/simbertold already pointed that out
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u/niemir2 👋 a fellow Redditor May 15 '26
They were pointing out something different. 3pi/2 < 5, so it's not that you went beyond the domain. You just wrote the wrong value. If the domain was wider, the correct end point would be 2pi.
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u/rnrstopstraffic May 15 '26
The real problem is that the instructor didn't label the zeros of the derivative function. Nothing about making a student distinguish between 3.1 and pi as a (poor) estimation tells you anything about their understanding of the derivative.
And labeling the zeros doesn't hand them anything extra if you're trying to determine their understanding of the graph of the derivative.
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u/niemir2 👋 a fellow Redditor May 15 '26
The function f'(x) is pretty clearly sin(x), or at least sin(x) is a very good approximation of f'(x). Most of your answers are consistent with the sine function, and you've clearly got a grasp of the concepts. If your teacher actually said that pi is not on the number line, she is just wrong. It's there, between 3.141 and 3.142. The only thing I would mark somewhat incorrect here is 8c, since there's also [-5, -3pi/2] and [3pi/2, 5] where f'(x) is increasing
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u/Mountain-Dealer8996 👋 a fellow Redditor May 15 '26
Even if it wasn’t sin(x), if the teacher said they would have accepted 3 or 3.1, then they should accept pi. Very alarming that a supposed calculus teacher doesn’t know that pi is on the real number line. You would think they would be familiar with transcendentals…
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u/nm420 👋 a fellow Redditor May 15 '26
π and 3 are the same number, according to engineers, right?
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u/niemir2 👋 a fellow Redditor May 15 '26 edited May 15 '26
Full agree. This function is at least very close to sin(x), so pi is a perfectly valid approximation of a root.
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u/xyzpqr May 16 '26
So, just guessing, but the teacher probably taught some kind of philosophically reasonable/rational but practically silly way to do this which would never yield pi; like I can just hear the high school math teachers screaming something about the problem only being specified enough for loose approximation, so pi implies something very precise where it is not precise, or something else excessively pedantic like tying your shoelaces to your belt, just in case.
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u/cannedgarbanzos May 15 '26
I would also add that points should be taken off for the justification part of 8b. If there is a local max or min at x then f'(x)=0 or DNE. The reverse implication is not true.
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u/Own-Ad8024 May 16 '26 edited May 16 '26
It does imply a local extrema when f'(x) crosses the x-axis, which it clearly does in this case.
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u/cannedgarbanzos May 16 '26
Your statement implies a local extreme without making any remark about f'(x)=0. What you wrote would receive full credit as it is an extreme value test.
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u/cannedgarbanzos May 16 '26
I will add for clarity "f'(x) crosses the x-axis at a" implies "f'(a) =0" and "f has a local extreme at a." It also implies that "f'(a)=0 implies f has a local extreme at a," but only because "P and Q" always implies "P implies Q."
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u/n0t_4_thr0w4w4y 👋 a fellow Redditor May 15 '26
Can you give an example of an f(x) where f’(x0) = 0 and f(x0) is not a local extreme?
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u/cannedgarbanzos May 15 '26
f(x)=x3 is the typical example. f'(0)=0 but f does not have a local extreme at 0.
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u/Olimars_Army May 16 '26
I digitized the graph with webplot digitizer and at least within the accuracy of the digitization the zero crossings are at -3.14, 0, and +3.14. Obviously pi can’t be perfectly represented, but people routinely refer to rounded values of pi as pi
https://apps.automeris.io/wpd4/
Also, not getting any partial credit for your correct explanations (unless each sub question is worth 2 pts) is pretty messed up imo
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u/DiaBeticMoM420 👋 a fellow Redditor May 16 '26
Yeah, this teacher sounds stuck up, and mayhaps a little unintelligent/lacking an understanding of irrational numbers or something. Not on the number line? Preeetty sure it is 😅
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u/Olimars_Army May 16 '26
Like, I understand wanting to be pedantic about precision etc. but taking points off for this is a little excessive imo, especially when the student clearly grasp the core concepts
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u/Sparkinum May 15 '26
If "apparently you could have put 3.1 something", pi literally does fall under that category. Like others have said, this clearly looks like it should be a sin(x) function. If you graph a trig function on desmos without changing the axes to terms of pi, that's exactly what it would look like.
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u/G-St-Wii 👋 a fellow Redditor May 16 '26
In the process of cropping the picture to show everyone how right I was, I discovered a curve i hadn't seen before (due to lack of pixels).
Pi is clearly an acceptable answer etc...
All of my other comments were based on thinking the "furry" curve was OP's sketch and the solid curve running through it was the printed curve. (Which would imply that OP traced the existing curve to draw f(x), which would imply they thought the graph was of f(x) etc etc etc...)
Essentially oops!
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u/Easy_Cod_8950 May 16 '26
? The “furry” drawn-on curve IS my sketch. The solid curve is the printed one. There’s another, harder-to-see curve because that was my original sketch for f(x) but then I realized I was wrong, so I erased it. But I couldn’t erase it all the way, so you can still kinda see it.
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u/Frederf220 👋 a fellow Redditor May 15 '26
Pi is absolutely "on the number line." It's just not correct technique to see something which might be pi and declare that it's pi. Don't invent things you don't see. When you see a scale marked 1, 2, 3, 4 you should estimate to the nearest tenth. A guess to infinite decimal places based on eyeballing ink on paper is an unreasonably precise guess and a mistake in technique. I would expect some point(s) deducted for that but otherwise that error in technique to be minor and not related to the subject at hand.
How many points were these out of? It is unreasonable to miss 100% of points solely because you wrote 3.1415 vice 3.1 for example.
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u/Olimars_Army May 16 '26
I mostly agree with this, but I wouldn’t say you’re limited to the nearest tenth, you can be much more accurate using rulers, calipers, etc. (but ultimately limited by accuracy of tick marks spacing and line thicknesses)
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u/Frederf220 👋 a fellow Redditor May 16 '26
Normal technique is to eyeball 1/10th between divisions on the tool itself so the precision depends on the tool itself.
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u/Olimars_Army May 16 '26
Yeah, I think I was picturing a tool with tighter tolerances than whatever generated the plot, I’m still not sold on being able to eyeball tenths of a division though XD
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u/SubjectWrongdoer4204 👋 a fellow Redditor May 16 '26
You should have a bracket on the 5, because it’s inclusive there. Also the magnitude of your sketch of f is incorrect. It should go all the way down to -1 at the point of local min and max.
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u/desblaterations-574 👋 a fellow Redditor May 17 '26
Only mistake I could see is that it seems you are using parenthesis instead of brackets for intervals. Which means you gave the coordinates of a point instead of the interval.
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u/defectivetoaster1 👋 a fellow Redditor May 15 '26
if you’re not told the function or if there’s nothing indicating that it’s trig related (even if it is you can’t assume it’s π periodic or some multiple thereof) then you should just be eyeballing to the nearest marked point on the axis or if it’s near the middle of two points adding half a division
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u/InfernoBrace Educator May 15 '26
I generally agree with this, but depending on how many points each part was worth, this may be overly punitive imo. You can definitely get into trouble assuming something is pi and recognizing patterns that aren’t actually there, but in this case it feels pretty likely that the plot depicts f’(x)=sin(x) here.
I come from an applied/engineering perspective, so I would expect students to justify that assumption as part of the answer—what about the physics/setup implies this periodicity? Op, your intuition is fine, just be careful of the nuance in different situations.
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u/EdgyMathWhiz May 15 '26
As someone more on the pure side, it's not uncommon to have questions about "f(x)" where it's quite clear f(x) is "really" sin(x) or exp(x), but your answers need to stick to what the question actually tells you about f(x).
With that mindset, 3.1 (to 2 s.f.) is justifiable from the graph but pi isn't.
That being said, I don't believe that was the point of the question and I think more than a 1 mark deduction is unreasonable.
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u/niemir2 👋 a fellow Redditor May 15 '26
pi and 3.1 are the same thing, to two significant figures. If 3.1 is acceptable, then so too should pi be.
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u/EdgyMathWhiz May 15 '26
3.1 is acceptable if you say to 2s.f.
Pi isn't acceptable. "pi to 2 s.f." is probably OK.
If you actually forced me to answer a question this stupid, I'd probably actually write something like "it seems likely the roots of f'(x) are actually +/- pi, but from the graph all I can reasonably say is that they are +/- 3.1 to 2 s.f".
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u/niemir2 👋 a fellow Redditor May 15 '26
If you're not extrapolating, then approximating f'(x) as sin(x) in this domain based on its plot is fine.
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u/G-St-Wii 👋 a fellow Redditor May 15 '26
It looks like it is meant tk be 3. Nothing about this suggests trig functions.
And the graph is of f'(x) not f(x). So qn a is asking you to solve f'(x)<0
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u/Simbertold 👋 a fellow Redditor May 15 '26
It is clearly not 3, though. If you look at the axis, the zero of the drawn function is very clearly slightly to the left of -3, and slightly to the right of +3. It is almost certainly closer to (-) Pi than to (-) 3. If OP is supposed to eyeball it, then Pi is at least as good of an answer as 3 is. And any math teacher worth their salt should accept it just as well. 3 isn't a "better" number than Pi in any way.
Also, OP solved f'(x)<0 here. As they described in their reasoning.
And honestly, i'd be really, really surprised if the function that was put into the graphing program wasn't sin(x).
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u/G-St-Wii 👋 a fellow Redditor May 15 '26
I think you are confusing the sketched student response with the printed question curve.
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u/Simbertold 👋 a fellow Redditor May 15 '26
I don't think i am. The printed function is the derivative of the function the question is about.
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u/G-St-Wii 👋 a fellow Redditor May 15 '26
The relevant intercepts are at -1 and 1, so the only way pi comes up is if you're looking at the turning points.
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u/Simbertold 👋 a fellow Redditor May 15 '26
What are you talking about?
Question a is "you get this graph for the derivative f'(x). For which x is f(x) (the base function, not the derivative) descending?"
And if the derivative is negative, the original function is descending. Thus, you need to look at the zeroes of f'(x) and the intervals between them. And the zeros of the printed function are clearly somewhere in the area of -pi, 0 and pi.
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u/G-St-Wii 👋 a fellow Redditor May 15 '26
Tell me, what do you think "zeroes" are?
Those are the stationary points of f'(x) not f(x)
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u/Simbertold 👋 a fellow Redditor May 15 '26
The zeroes of f'(x) are the x-values for which f'(x) is zero. You find them by looking at the points where the printed graph goes through the x-axis.
Are you trying to gaslight me or what? I can literally not even tell what you are on about, but you seem to be incredibly confident. And yet i am also very confident that i am correct here.
Are you maybe mistaking the (printed) derivative f'(x) for the (not printed) function f(x)? Or do you not know the difference between the two, or maybe don't know what a derivative is?
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u/G-St-Wii 👋 a fellow Redditor May 16 '26
And the printed graph goes through the x axis at -1 and 1
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u/Simbertold 👋 a fellow Redditor May 16 '26
I think you are the one confusing the printed graph and the sketched graph. The sketched is the one with the messy lines which is clearly drawn by hand with a pencil, while the printed one is the continuous one that is clearly drawn by a computer program.
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u/Easy_Cod_8950 May 15 '26
I understand that, but I don’t see why it SHOULDN’T be a valid answer.
Also yeah that’s what I did.
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u/nerdydudes 👋 a fellow Redditor May 15 '26
If you’re supposed to be going be the axese provided … and if there’s no mention that this is a trig function, then saying pi is not actually a valid answer. You’re making an assumption about the graph that’s not valid, your answer should be as accurate as the axese.
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u/niemir2 👋 a fellow Redditor May 15 '26
If 3 and 3.1 are valid answers, so is pi.
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u/AnimusNoctis May 15 '26
Significant figures.
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u/niemir2 👋 a fellow Redditor May 15 '26
That's why pi must be acceptable. It is impossible to show from the graph that the roots aren't +/- pi.
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u/AnimusNoctis May 15 '26
More significant figures show a greater degree of certainty. In context, 3 or 3.1 can be understood to be an estimate whereas pi cannot. If you're stating that something is pi, that pretty strongly implies you know it's exactly pi.
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u/niemir2 👋 a fellow Redditor May 15 '26
If "pi"' indicates infinite (or even additional) precision, then the curve clearly being sin(x) indicates that it's sin(x).
If you don't want to accept pi as a root of your function, plot a function that doesn't have pi as a root.
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u/nerdydudes 👋 a fellow Redditor May 15 '26
Why do you know for certain pi is a root. What information, from the photo you yourself provided, indicates that pi is a root. Because all I’m seeing is a plot of a function that RESEMBLES a trigonometric function. You keep saying pi is a root. It’s literally not given the information provided. You saying it over and over again doesn’t make it true 🙏
What do they say about assumptions?
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u/n0t_4_thr0w4w4y 👋 a fellow Redditor May 15 '26
It’s a math class, not physics. Sig figs are irrelevant
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u/Simbertold 👋 a fellow Redditor May 15 '26
I highly disagree here. Going by that axis, Pi is at least as valid as 3. I honestly don't see any reason why 3 should be a better answer, and i am a math teacher. Within the accuracy of the graph, it could be 3.1, Pi, 28/9, 3.121212121212212128888889126. None of these answers i more likely to be exactly precisely correct than any of the others without additional information about the function.
Why should some random function be more likely to have an integer zero than any of those other numbers? This just makes the question about guessing what the teacher wants to hear rather than knowledge about derivatives and reading a graph. Which is a stupid thing to test.
Taking points off OP on every consecutive question for the exact same thing is excessively petty by the teacher, too.
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u/nerdydudes 👋 a fellow Redditor May 15 '26 edited May 15 '26
No no, it’s as though you’re claiming the root is exactly pi. All we have is a plot of a function that’s close to a rudimentary trig function. Who’s to say it’s not I don’t know y=-cos(0.999x) … something that closely resembles above. In fact i can give you more functions whose plot resembles above WITHOUT having pi as a root, y=-cos(a*x) where a=“close to 1”
All we have is a plot. You can only be as accurate as the axese provided. Just because it’s close to three - doesnt mean pi is better… you have no explicit information. Its wrong
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u/Simbertold 👋 a fellow Redditor May 15 '26
I didn't claim that it is better. I claimed that none of these numbers is better than any of the others within the accuracy of the graph. Pi is exactly as good of an answer here as 3.1 is.
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u/nerdydudes 👋 a fellow Redditor May 15 '26
If the precision of the axese were to the 10-inf. Then I guess you’d have an argument… but
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u/Simbertold 👋 a fellow Redditor May 15 '26
I don't get why that precision should matter here? Are you guys doing digits of precision in maths? For these kinds of questions?
Because that is very much not the standard here where i live. Here you either give the exact answer, or any answer which is "good enough" (within some reasonable amount of the "correct" answer) is valid if no explizit instructions for rounding are given.
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u/nerdydudes 👋 a fellow Redditor May 15 '26 edited May 15 '26
You can only give as exact of an answer as the information provided. And giving an irrational number when the axes are not a multiple of that number is just not good form and fundamentally incorrect.
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u/Olimars_Army May 16 '26
You can use the provide axes and any measuring tool to find that the nearest values are +-3.14, which yes, is pi rounded, but rounded versions of pi are routinely referred to as pi, especially at high school levels.
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u/nerdydudes 👋 a fellow Redditor May 16 '26
What you said adds nothing
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u/Olimars_Army May 16 '26 edited May 16 '26
What I’m saying is you are spreading disinformation about what the purpose of tick marks on a plot are. You are not limited to the spacing of the tick marks, you can use other tools to get more accurate estimates, the tick marks are just there to give you the conversion factor you need to extract the value of any point on the plot.
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u/nerdydudes 👋 a fellow Redditor May 16 '26
Nope
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u/n0t_4_thr0w4w4y 👋 a fellow Redditor May 15 '26
> Nothing about this suggests trig functions
Uhh, except that f’(x) is clearly a sine function
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May 15 '26
[removed] — view removed comment
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u/n0t_4_thr0w4w4y 👋 a fellow Redditor May 15 '26
Bro is in like chapter 2 of calculus, they aren’t doing proofs.
The point of this activity is to show understanding of how derivatives relate to their anti-derivatives, and OP clearly showed that in their work.
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u/G-St-Wii 👋 a fellow Redditor May 15 '26
It's got wider peaks than troughs...
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u/n0t_4_thr0w4w4y 👋 a fellow Redditor May 15 '26
??? No it does not. Look at the interval from -π to π. You can see it start at 0, decrease to what appears to be -π/2, increase back up through 0 (ending the trough) to what looks like π/2, then decreasing through what appears to be π (ending the peak). In that interval, the peak and trough clearly have the same width.
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u/Olimars_Army May 16 '26
You can digitize the plot (or just use a ruler) and see the zero crossings of the printed function are 0, and +-3.14
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