If $f(x) = 2x^3 - 3x^2 - 12x + 5$ and $x \in [-2, 4]$,then the maximum value of the function occurs at which value of $x$?

The maximum slope of the curve $y = \frac{1}{2} x^{4} - 5 x^{3} + 18 x^{2} - 19 x$ occurs at the point

What is one of the maximum values of $f(x) = x + \sin(2x)$ in the interval $[0, 2\pi]$?

If $f(x) = (\sin^4 x + \cos^4 x)$,$0 < x < \frac{\pi}{2}$,then the function has a minimum value of $ . . . . . . $ at $x = . . . . . . $.

Let $f: R \rightarrow R$ be a polynomial function of degree four having extreme values at $x=4$ and $x=5$. If $\lim _{x \rightarrow 0} \frac{f(x)}{x^2}=5$,then $f(2)$ is equal to:

Let the set of all values of $p$,for which $f(x) = (p^2 - 6p + 8)(\sin^2 2x - \cos^2 2x) + 2(2 - p)x + 7$ does not have any critical point,be the interval $(a, b)$. Then $16ab$ is equal to ..........