Question

Math question

Answer 1

I'm sorry, I think C. is a wrong option

Answer 2

hint:
the first derivative of your function is:
\[f'\left( x \right) = 3\left( { - {x^2} + 1} \right)\]
and such first derivative is positive, when:
\[ - {x^2} + 1 > 0\]
or, equivalently, when:
\[{x^2} - 1 < 0\]
The solution of the last inequality is:
\[S = \left\{ {x \in \mathbb{R}| - 1 < x < 1} \right\}\]

as we can see, we have a local, or relative maximum, at \(x=1\)