Local maximum and local minimum values of the function $f(x) = (x - 1)(x + 2)^2$ are

If $f(x) = x^3 + ax^2 + bx + c$ has a minimum at $x = 3$ and a maximum at $x = -1$,then:

$A$ wire of length $20$ units is divided into two parts such that the product of one part and the cube of the other part is maximum. Then,the product of these parts is:

The difference between the maximum and minimum values of $f(x) = x^4e^{-x^2}$ for all $x \in R$ is:

If the extreme value of the function $f(x) = \frac{4}{\sin x} + \frac{1}{1 - \sin x}$ in the interval $[0, \frac{\pi}{2}]$ is $m$ and it exists at $x = k$,then $\cos k =$

Let $f : R \rightarrow R$ be a function defined by $f(x) = ||x+2|-2|x||$. If $m$ is the number of points of local minima and $n$ is the number of points of local maxima of $f$,then $m+n$ is