Average fixed cost of the cost function C(x) = 2x³ +5x² - 14x +21 is _______.

Marginal revenue of the demand function p = 20–3x is _______.

For the cost function C =\(\frac { 1 }{ 25 } { e }^{ 5x }\), the marginal cost is _________.

Instantaneous rate of change of y = 2x² + 5x with respect to x at x = 2 is _________.

If the average revenue of a certain firm is Rs. 50 and its elasticity of demand is 2, then their marginal revenue is _________.

The cost function of a firm is \(C={1\over3}x^3-3x^2+9x\). Find the level of output (x > 0) when average cost is minimum.

For the demand function x = \(\frac { 25 }{ { p }^{ 4 } } ,1\le p\le 5\), determine the elasticity of demand

The demand and cost functions of a firm are x = 6000 – 30p and C = 72000 + 60x respectively. Find the  level of output and price at which the profit is maximum.

Find the interval in which the function f(x) = x² – 4x + 6 is strictly increasing and strictly decreasing.

If u = log(x²+y²), then show that \(\frac { { \partial }^{ 2 }u }{ { \partial x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ \partial { y }^{ 2 } } =0\)

Verify Euler’s theorem for the function \(u=\frac{1}{\sqrt{x^2+y^2}}\)

The demand and the cost function of a firm are p = 497 - 0.2x and C = 25x +10000 respectively. Find the output level and price at which the profit is maximum

A monopolist has a demand curve x = 106 – 2p and average cost curve AC = 5 + \(\frac { x }{ 50 } \) where p is the price per unit output and x is the number of units of output. If the total revenue is R = px, determine the most profitable output and the maximum profit.