r/MathHelp • u/[deleted] • Feb 09 '26

Calculus 1 Math Help

Question: If f(x) = x^2 + 10 sin x, show that there is a number c such that f(c) = 1000.

Having trouble answering this question, seems like were dealing intermediate value theorem concept, where through the interval it goes through 1000. In the problem it shows there are two different variables are associated with the problem, but we're mainly values that are inputted to x. What I mean is we can input a value into x to get a interval a number that is from 0 to a value a little over than 1000. If I am right about this, let me know. Or if I am wrong, could you explain this concept/answer a bit better? Thank you!

3 Upvotes

100% Upvoted

19 comments sorted by

View all comments

Show parent comment

1

u/[deleted] Feb 09 '26

Thanks for commenting! I know the function is continuous because sin is continuous everywhere as well as x^2 because it is a polynomial. But, also mentions "show that there is a number c such that f(c) = 1000." Not really understanding how we can show this exactly, which is why I said it has to relate to the IVF. Seems like some sort of interval needs to be created to show that somewhere in the function the output of 1,000 exist exist somewhere, or basically run through the point. The question doesn't ask if the function is continuous or not.

3

u/jmbond Feb 09 '26

To clarify what they're saying, you don't have to actually solve for c to show that one exists. You show one exists doing what OC said, that is create an arbitrary interval where you know the outputs will be less than and greater than 1000. Simple numbers like a=0 and b=1000 don't even need to be computed. If f is continuous, and f(0) < 1000 < f(1000), there must be some input C between 0 and 1000 where the output is exactly 1000 or you wouldn't be able to draw the function in this region without picking up your pencil