The demand for a certain product is represented by the function $p = 300 + 25x - x^2$ (in rupees), where x is the number of units demanded and p is the price per unit, then the marginal revenue when 15 units are sold, is

A car is moving along the curve $y = x^3 + 12$. The point(s) on the curve at which the rate of change of its y-coordinate at a certain time is 3 times the rate of change of its x-coordinate is/are

If $x$ is real, the minimum value of $x^2 - 8x + 20$ is

The appropriate change in the volume V of a cube of side $x$ metres caused by increasing the side by 2% is :

Function $f(x)=\sin3x, x \in \left[0,\frac{\pi}{2}\right]$ is decreasing in the interval

Let $f(x) = x^3 - 6x^2 + 9x - 8$ be a function, then which of the following statements are TRUE?

(A) $f'(x) = 3(x - 1)(x - 3)$

(B) The critical points of the function are $x = 1$ and $x = 3$

(C) $x = 1$ is the point of local minimum

(D) The local maximum value is $-4$

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: