The absolute maximum value of the function $f(x) = 2x^3 - 15x^2 + 36x + 7$ on the interval [1,5] is

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:

The demand function for a certain product is represented by the equation: $p = 20 + 5x - 3x^2$, where $x$ is the number of units demanded and $p$ is the price per unit (in Rs.), then the marginal revenue when 2 units are sold is:

Which of the following statements are true?

(A) The function $f(x) = \frac{x^4}{4} - \frac{4}{3}x^3 + \frac{x^2}{2} + 6x$ has 3 critical points.

(B) The function $f(x) = |x| + 3$ has no minimum value.

(C) A local maximum value is always the absolute maximum value.

(D) $f(x) = x^2$ has minima at $x=0$.

Choose the correct answer from the options given below:

The maximum value of the function $f(x) = x^2(60 - x)$ in [20, 80] is:

The minimum value of $f(x) = |2x - 1|$ is

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