An open box is made from a cardboard measuring 12cm x 12cm by cutting off equal squares from the corner and turning up the side. Then maximum possible volume of the box would be:

If the interval in which the function $f(x) = 4x^3 - 6x^2 - 72x + 30$ is strictly decreasing, is (a,b) then a+b is equal to

A cylindrical drum of radius 7 cm and height 2 m is being kept in a vertical position filled with milk. If the milk is leaking at 14 cm³/sec from its lower base, then the rate of decrease in the level of milk is:

[Take $\pi = \frac{22}{7}$]

If the function $f(x) = x^2 - ax - 2$ is strictly decreasing on $(2, 3)$ then $a$ lies in the interval.

Let f be a function defined by $f(x) = 2x^3 - 3x^2 - 36x + 2$, then which of the following are correct?

(A) The critical points of f(x) are -2 and 3.

(B) The function f(x) increases in the interval $(3, \infty)$

(C) The function f(x) decreases in the interval (-2,3)

(D) The function f(x) increases in the interval (-2,3)

Choose the correct answer from the options given below:

The interval, on which the function $f(x) = x^2e^{-x}$ is increasing, is equal to

Based on above information answer the following question :

$\frac{dA(x)}{dx} =$