or the function, find all critical points or determine that no such points exist.
f (x) = sin2 x
We can rewrite the function as
f (x) = (sin x)2,
which means we need the chain rule to take the derivative of this function.
f '(x) = 2(sin x)(cos x)
The derivative f'(x) is never undefined, but is 0 whenever either sin or cos is 0 - that is, at every multiple of π/2. So these are our critical points. The graph looks like this: