Answer
No local maximum value or minimum value
Work Step by Step
Let us take the derivative of the given function:
$f'(x)= 3x^2+2x+\sec^2 x$ for all $x \neq \pi/2+k \pi$
Thus, the function $f(x)$ does not not have any critical points or real solutions.
Thus: no local maximum value or minimum value.
