Question

Find any critcal numbers of the function:
h(x)=sin^2x+cosx 0 15 years ago

Answer 1

take derivative and set it equal to zero

Answer 2

you are gonna have to use the chain rule with this problem

Answer 3

or maybe rewrite using double angel therm

Answer 4

The critical points of a function are the points where the derivative is zero and the points where the function is not differentiable. Since this function is differentiable everywhere in its domain (if the domain was\[[0, 2\pi],\]a closed interval, you would have to check the end points of the interval too) the only points that matter are where the derivative is zero.
\begin{eqnarray*}&&h'(x) = 2\sin(x)\cos(x)-\sin(x) = \sin(x)(2\cos(x) - 1) = 0 \\ \Rightarrow&& \sin(x) = 0 \lor \cos(x) = \frac{1}{2} \Rightarrow x = \pi \lor x = \frac{\pi}{3} \lor x = \frac{5\pi}{3}.\end{eqnarray*}