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

The function $f(x) = \frac{4x^2+1}{x}$ is decreasing in

(A). $\left(\frac{-1}{2}, \frac{1}{2}\right)$

(B). $\left(-\infty, \frac{-1}{2}\right)$

(C). $\left(0, \frac{1}{2}\right)$

(D). $\left(\frac{-1}{2}, 0\right)$

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The function $f(x) = x^4 - 2x^2$ is increasing on

The interval in which the function $f(x) = 2x^3 + 3x^2 - 12x + 1$ is strictly increasing is -

The difference of absoulte maximum (largest) and absoulte minimum (smallest) values of the function $f(x) = 12x^{4/3} - 6x^{1/3}, x \in [-1, 1]$ is

The angle of intersection between the curves $y = 4 - x^2$ and $y = x^2$ is :

Let $f(x) = x^2 + \frac{250}{x}$ be any function defined on $\mathbb{R} - \{0\}$, where $\mathbb{R}$ is the set of real numbers. Then which of the following are TRUE?

(A) $f'(x) = 2x + \frac{250}{x^2}$

(B) $x = 5$ in the only critical point of $f(x)$

(C) minimum value of $f(x)$ is 75

(D) maximum value of $f(x)$ is 50.

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