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

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:

If maximum value of $f(x) = 2x^3 + 3x^2 - 6ax + 10$ occurs at $x = -3$, then the value of $\alpha$ is ____

If $f(x) = x^4 - \dfrac{2x^3}{3}$, then $f(x)$ is

A. increasing in $\left(\dfrac{1}{2}, \infty\right)$

B. decreasing in $\left(\dfrac{1}{2}, \infty\right)$

C. increasing in $(-\infty, 0)$

D. decreasing in $(-\infty, 0) \cup \left(0, \dfrac{1}{2}\right)$

Choose the correct answer from the options given below:

A square board of side 36cm is made into a box without top by cutting a square from each corner and folding up the flaps to form a box then maximum volume of the box is

The total cost $c(x)$ associated with the production of $x$ units of an item is given by $c(x) = 0.001x^3 + 0.06x^2 + 20x + 500$. The marginal cost when 10 units are produced is:

Let height and radius of a right circular cylinder are $h$ and $r$ respectively. If it is open at the top, having a given surface area and greatest volume, then