or the function, find all critical points or determine that no such points exist.

*f* (*x*) = sin^{2} *x*

Answer

*f* (*x*) = sin^{2} 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: