The maximum value of $f(x) = x^{50} - x^{20}$ in the interval $[0,1]$, is

The function $f(x) = x^3 + 2x^2 - 1$ is

(A) increasing in $\left(\dfrac{-4}{3}, 0\right)$

(B) decreasing in $\left(\dfrac{-4}{3}, 0\right)$

(C) increasing in $\left(-\infty, \dfrac{-4}{3}\right)$

(D) increasing in $(0, \infty)$

Choose the correct answer from the options given below:

A balloon which always remains spherical is being inflated by pumping in 900 cubic cm of gas per second. The rate at which the radius of the balloon increases when the radius is 15 cm is

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

The function, $f(x) = x - \frac{1}{x}$ is

The revenue function is given by $R(x)=150x-2x^2-x^3$, where $x$ is the number of units demanded, then the marginal revenue when 5 units are sold, is :

The sum of two positive numbers is 60. If the sum of their squares in minimum, then the absolute value of the difference of their cubes is