Answer
No local maximum value or minimum value
Work Step by Step
Need to take the derivative of the given function as follows:
$f'(x)= 3x^2+2x+\sec^2 x$ for all $x \neq \dfrac{\pi}{2}+k \pi$
Here, the function $f(x)$ does not contain critical points or real solutions of the function.
This implies that we have found no local maximum value or minimum value.
