Got some questions:(adsbygoogle = window.adsbygoogle || []).push({});

Say I have the function f(x) = x*sin(3x/4).

1. What is the relationship between the sign of f'(x) and the graph of f(x)?

2. What can be observed about the relative locations of the roots of f(x) and f'(x)?

3. If f has zeros at r1 and r2 and if f is differentiable on the interval [r1, r2], then f' must...?

I cannot for the life of me figure out any of these. For the first question, I'm guessing that f increases whenever f' is positive and f decreases when f' is negative?

Thanks for any assistance.

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# Derivatives and Zeros

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