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In the following problem, the range of the periodic function f(x) is [a, b]. Find b-a. f(x)=sin(x)cos(x)

I know the derivative, I just don't know what to do from there.

f'(x)=-sin^{2} x+cos^{2} x = cos(2x)

Disclaimer: This is for AP Calculus AB

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In the following problem, the range of the periodic function f(x) is [a, b]. Find b-a. f(x)=
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