The problem reads like this:

Is it possible for a continuous smooth function g(x) on the domain [-6, 6] to have an absolute maximum at a point x_{0}in [-6, 6] without the derivative f'(x_{0}) 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'(x_{0}) = 0. Am I correct?