Given that the total cost function for x units of a commodity is $C(x) = \dfrac{x^3}{4} + 4x^2 - 8x + 20$. Then the marginal cost when $x=4$ is:

The value of the integral $\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx$ is :

If $C(x) = x^3 - \frac{5}{2} x^2 + 10$ represents the total cost of producing x unit by car manufacturing company. The slope of the marginal cost curve at $x = 3$, will be

If the cost function $C(x)$ of producing $x$ units of a commodity is given as $C(x) = x^3 - 60x^2 + 13x + 50$, then the level of output for which the marginal cost is minimum is

If $x = 2at, y = at^2$, where 'a' is a constant, then $\frac{d^2 y}{dx^2}$ at $x = 2$ is :

If the sum of two positive numbers is 25 and their product is maximum when divided in the ratio of cubes of one and squares of the other, then the numbers are:

The value of the integral $\int_{-3}^{3} (x^3 - x) dx$ is :