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Question

Show that the function f(x)=sin(2x+π/4) is decreasing on (3π/8,5π/8)

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Solution

We have

f(x)=sin(2x+π/4)f(x)=2cos(2x+π/4)

Now, x(3π/8,7π/8)3π/8<x<5π/83π/4<2x<5π/4π<2x+π/4<3π2

2cos(2x+π/4)<0f(x)<0

So, f(x) is decreasing on (3π/8,7π/8)

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