The rate of change of area of a circle with respect to its circumference when radius is 4cm, is

The slope of the tangent to the curve $x = at^2$, $y = 2at$ at 't' is :

In which of the following intervals, the function $f(x) = -x^2 - 2x + 15$ is decreasing?

The function $f(x) = 2x^3-15x^2+36x+4$ has local maxima at $x=$

The volume of a cube is increasing at the rate of 27 cm$^3$/s. How fast is the surface area increasing when the length of the cube is 12 cm.

The function $f(x) = 4 - 3x + 3x^2 - x^3$ is (Here $\mathbb{R}$ is set of real numbers)

Let $f(x) = 4x^3 - 18x^2 + 27x - 5$, $x \in R$. Then which of the following statements are TRUE?

(A) $f''(x) = 24x - 36$

(B) f has local maxima at $x = \frac{3}{2}$ but no minima

(C) f has neither maxima nor minima

(D) f has both maxima and minima

Choose the correct answer from the options given below: