The supply function of a commodity is P = $x^3+2x+18$. When 4 units of commodity are sold , then producer surplus is:

If $y = \log_e \left(\frac{x^3}{e^3}\right)$, then $\frac{d^2 y}{d x^2}$ is equal to

Let $f : R \to R$ be defined such that $f(x) = 16x^2 - 16x + 12$

(A) Maximum value of $f(x)$ is 8

(B) Minimum value of $f(x)$ is 8

(C) Minimum value of $f(x)$ is 16

(D) No maximum value of $f(x)$

Choose the correct answer from the options given below :

If $x^3 + y^3 = xy$, then $\frac{dy}{dx}$ is equal to :

The order and degree Of the differential equation $\frac{d^2 y}{dx^2} + 2 e^{-x} = 0$, respectively are

If $t = e^{2x}$ and $\log_e t^2$, then $\frac{d^2y}{dx^2}$ is :

For a manufacturer, total cost function is given by $C = \frac{x^2}{25} + 2x$. Which of the following are correct ?

A. 2.6 is the marginal cost when 5 units are produced.

B. $\frac{2x}{25} + 2$ is the marginal cost function.

C. $\frac{x}{25} + 2$ is the average cost function.

D. 2.4 is the marginal cost when 5 units are produced.

E. $\frac{x}{25} + 1$ is the average cost function.

Choose the correct answer from the options given below: