A spherical ice ball is melting at the rate of 100 $\pi$ cm³/min. The rate at which its radius is decreasing when its radius is 15 cm, 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

The rate of change of volume of a sphere with respect to its surface area, when radius is 4 cm, is equal to

Consider the function $f(x) = x^4 - 2x^2$, then which of the following are TRUE?

A. $f(x)$ is increasing on $(-1,0)$

B. $f(x)$ is decreasing on $(0,1)$

C. $f(x)$ is increasing on $(-\infty,-1)$

D. $f(x)$ is decreasing on $(1,\infty)$

Choose the correct answer from the options given below:

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

If the minimum value of $a$ is $-\frac{k}{2}$ such that the function $f(x) = x^2 + ax + 5$ is increasing in [1, 2]. Then value of $k$ is

If the function $f(x)$ defined by $f(x) = x^3 - 3x + 100, (x \in \mathbb{R})$, (Where $\mathbb{R}$ is set of real numbers), then $f(x)$ has