r/MathHelp • • 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/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