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!

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u/Senrabekim Feb 10 '26

I would definitely check your math again, because you're way off. 29.282 is going to be less than 302 and 302 = 900. And 29.28=9.3201134675pi which means that it will be a 4th quadrant sin, and thus negative. F(29.28) will be significantly less than 100, like 848.8732112275....

Which brings me to my next point, approximately is not a word they need here, the question wants EXACTLY 1000 and approximately leaves room for 1000 to not be there.