1. ## Differential Calculus

Is it possible for a continuous smooth function g(x) on the domain [-6, 6] to have an absolute maximum at a point x0 in [-6, 6] without the derivative f'(x0) being 0? If so, draw an example of such a function.

Here are my workings:
I think that it is not posible to have absolute maximum without being f'(x0) = 0. Am I correct?

2. ## Re: Differential Calculus

How about considering a monotonic increasing function such as $f(x)=x^3$ over the domain? Notice that $f(x)$ is maximized when $x_0 = 6$, but $f'(6)=2(6)^2 \neq 0$. The key here is that the absolute maximum can exist on the boundary in this case, but if the domain is $(-6,6)$ then it won't happen.