The total cost function for $x$ units of a commodity is given by $C(x) = \frac{25x^3}{3} - 75x^2 + 48x + 34$. The output $x$ at which the marginal cost is minimum is :

The minimum value of $f(x) = 4x^3 - 48x + 105$ in the interval [1,3] is :

If the total cost and total revenue of a company that produces and sells $x$ units of a particular product are $C(x) = 5x + 350$ and $R(x) = 50x - x^2$ respectively, then which of the following is/are the breakeven values:

(A) $x = 10$

(B) $x = 25$

(C) $x = 45$

(D) $x = 30$

Choose the correct answer from the options given below:

Two positive numbers $x$ and $y$ such that $x + y = 60$ and $xy^3$ is maximum are :

Match List - I with List - II.

Choose the correct answer from the options given below :

If $(x+ 1) e^y = 1$ , then :

If $R(x)$ is the total revenue received and $C(x)$ is the total cost incurred in the production of x units of a commodity, then the profit function $P(x)$