Find the elasticity of supply for the supply function x = 2p² - 5p + 1, p > 3.

For the function y = x³ +19 find the values of x when its marginal value is equal to 27.

A firm produces x tonnes of output at a total cost of C(x) = \(\frac { 1 }{ 10 } \)x³ - 4x² - 20x + 7 find the
(i) average cost function
(ii) average variable cost function
(iii) average fixed cost function
(iv) marginal cost function and
(v) marginal average cost function.

Find the elasticity of demand in terms of x for the following demand laws and also find the output (x), when the elasticity is equal to unity. 
(i) p = (a - bx)²
(ii) p = a - bx²

Find the stationary value and the stationary points f(x) = x² + 2x – 5.