f(x)=cos2(x)
f'(x) = -2•cos(x)sin(x)
0 = -2•cos(x)sin(x)
cos(x)=0 or sin(x)=0
the local extrema on the interval [-π,π] are:
x = -π/2,0,π/2
Intervals of x Behavior
-π < x <-π/2 decreasing (-)
at x = -π/2 local minimum
-π/2 <x < 0 increasing (+)
at x=0 local maximum
0<x<π/2 decreasing (-)
at x=π/2 local minimum
π/2 < x < π increasing (+)
Joel L.
tutor
Be careful. What you'll get on the derivative when you make it equal to zero are just the local extrema. In the instruction, It's asking which parts are decreasing and which are increasing on the given interval. Good luck to your studies.
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04/29/21
Joel L.
tutor
By the way for the intervals of x, I put inequalities instead of interval notation. It's better that way so that you'll not get confused which are point coordinates and which are intervals when they get mixed up. I advise you to do the same.
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04/29/21
Maggie D.
Thank you! I had it wrong... I was showing the increase/decrease of the derivative04/29/21