Applications of Differentiation Three Marks Questions

11th Standard

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Time : 00:45:00 Hrs
Total Marks : 30
10 x 3 = 30
1. 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.

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

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

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

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

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

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

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

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

10. 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]