Find the elasticity of demand in terms of x for the demand law \(p={(a-bx)^{1\over 2}}.\) Also find the values of x when elasticity of demand is unity.

Find the elasticity of supply for the supply law \(x={p\over p+5}\) when p = 20 and interpret your result.

Revenue function ‘R’ and cost function ‘C’ are R = 14x - x² and C = x (x² - 2). Find the
(i) average cost function 
(ii) marginal cost function,
(iii) average revenue function and
(iv) marginal revenue function.

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

For the production function P = \(4L^{ \frac { 3 }{ 4 } }K^{ \frac { 1 }{ 4 } }\) verify Euler’s theorem.

Find the stationary points and stationary values of the function f(x) = x³ - 3x² - 9x + 5.

Show that the function x³ + 3x² + 3x + 7 is an increasing function for all real values of x.

Separate the intervals in which the function x³ + 8x² + 5x - 2 is increasing or decreasing.

Find the maximum and minimum values of the function x² + 16/x

For the production function P= 5(L)^0.7(K)^0.3.Find the marginal productivities of Labour (L) and Capital (K) when L = 10, K = 3 [Use (0.3)^0·3 = 0.6968; (3.33)^0·7 = 2.2322]