Explanation:
A critical point is a point where the function is undefined or its derivative is zero or undefined.
For this function, it is always defined in the given domain. We have to see the derivative:
[tex]\frac{dg(x)}{dx}=g^{\prime}(x)=-3\sin x[/tex]
It is also always defined in the domain, but it has a zero:
[tex]\begin{gathered} -3\sin x=0 \\ \sin x=0 \\ x=n\pi\text{ , }n\in\Z \end{gathered}[/tex]
n is ...-3, -2, -1, 0, 1, 2, 3, ...
So there's only one critical point in the domain, and that's x = 0.
Answer:
There's only 1 critical point in the domain: 0
