The absolute maximum value of the function $f(x) = 2x^3 - 3x^2 - 36x + 9$ defined on $[-3, 3]$ is

$A$ triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having a fence are of the same length $x$. The maximum area (in sq. units) enclosed by the park is

Show that the height of the cylinder of greatest volume which can be inscribed in a right circular cone of height $h$ and semi-vertical angle $\alpha$ is one-third that of the cone and the greatest volume of the cylinder is $\frac{4}{27} \pi h^{3} \tan^{2} \alpha$.

Let $R$ denote the set of all real numbers. Let $f: R \rightarrow R$ be defined by $f(x)=\begin{cases} \frac{6x+\sin x}{2x+\sin x} & \text{if } x \neq 0 \\ \frac{7}{3} & \text{if } x=0 \end{cases}$. Then which of the following statements is (are) True?
$(A)$ The point $x=0$ is a point of local maxima of $f$
$(B)$ The point $x=0$ is a point of local minima of $f$
$(C)$ Number of points of local maxima of $f$ in the interval $[\pi, 6\pi]$ is $3$
$(D)$ Number of points of local minima of $f$ in the interval $[2\pi, 4\pi]$ is $1$

$A$ wire of length $8 \text{ units}$ is cut into two parts which are bent respectively in the form of a square and a circle. The least value of the sum of the areas so formed is

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