HELP PLEASE!!!! locate the critical points and classify them as stationary points. f(x)=sin^2x, 0

Question

HELP PLEASE!!!! locate the critical points and classify them as stationary points. f(x)=sin^2x, 0<x<2pi

anonymous · Answer

Do you know how to find critical points?

anonymous · Answer

To find critical points you take the derivative and set it to 0 and solve for x, so take the derivative of your problem then set it = 0 and then solve for x.

rajee_sam · Answer

$$Sin ^{2}X$$

rajee_sam · Answer

is it ?

anonymous · Answer

oh no its sin^2 2x

rajee_sam · Answer

OK to find the critical points like onegirl said set your first derivative to zero and find the values of x for which it will be = 0

rajee_sam · Answer

$$f'(x) = 2\sin2xcos2x . 2 = 4 \sin2x \cos2x$$

rajee_sam · Answer

$$4 \sin2xcos2x = 0$$ means either sin2x = 0 or cos2x = 0

rajee_sam · Answer

your interval given is 0 to 2pi

anonymous · Answer

how did you get that first derivative?

anonymous · Answer

was it with a chain rule?

rajee_sam · Answer

yes

rajee_sam · Answer

sin^2 2x - first do the power 2 sin2x, now do the sin2x, which will cos2x and then you have to do the 2x which is 2

anonymous · Answer

oh okay i see now

rajee_sam · Answer

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If you see the curve slope is zero at $$\pi/4 , 3\pi/4, 5\pi/4, 7\pi/4$$