Find the total number of local maxima and local minima of the function $f(x) = \begin{cases} (2+x)^3, & -3 < x \leq -1 \\ x^{2/3}, & -1 < x < 2 \end{cases}$

If $f(x) = \int\limits_0^x {{e^{\frac{{ - {t^2}}}{2}}}} \left( {1 - {t^2}} \right)\,dt$,then $f(x)$ is minimum at $x = \dots$

The minimum value of the polynomial $x(x + 1)(x + 2)(x + 3)$ is

Find the local maximum and local minimum values for the function $f(x) = \sin x - \cos x$ where $0 < x < 2\pi$.

$A$ sector is removed from a metallic disc and the remaining region is bent into the shape of a circular conical funnel with volume $2 \sqrt{3} \pi$. The least possible diameter of the disc is

What are the minimum and maximum values of the function $f(x) = x^5 - 5x^4 + 5x^3 - 10$?