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Question

Given f(x)=cos2x , find whether f(x) is increasing or decreasing in the range [0,π2].

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Solution

f(x)=cosx
differentiating w.r.t x
f(x)=2cosx.(sinx)=sin2x
here,
0xπ202xπsin2x0sin2x0f(x)0
f(x) is decreasing

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