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

Match List - I with List - II.

Choose the correct answer from the options given below :

$\int_1^4 x^3\log x\, dx$ is equal to:

The total cost of producing $x$ generators is given by

TC = $x^3 - 60x^2 + 1500x + 2000$.

The Marginal Cost (MC), when $x = 10$ units is:

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 $y = \log\left(\frac{x^5}{e^5}\right)$, then $\frac{d^2y}{dx^2}$ is,