A product costs the manufacturer ₹ 20 per unit. The demand function is given by $p(x) = 1000 - 20x$, then the quantity for maximum profit is :

Match List - I with list- II

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The second order derivative of the function $y=\log(4x^3+6)$ with respect to 'x' 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

The value of a for which the function $f(x) = a^x$ is increasing on R are given by :

Which of the following statements are true?

(A) The break-even point is the level of production where the revenue from sales is equal to the cost of production and marketing.

(B) If R is the total revenue collected by a company when it sells $x$ units of a product at a price of p per unit, then R is given by $R=px$.

(C) Let $C=C(x)$ be the total cost of producing and marketing $x$ units of a product, then marginal cost, $MC=\frac{dC}{dx}$.

(D) If AC is the average cost, then $AC=\frac{x}{C}$.

Choose the correct answer from the options given below:

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