#### Applications of Differentiation Book Back Questions

11th Standard

Reg.No. :
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Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. Average fixed cost of the cost function C(x) = 2x3 +5x2 - 14x +21 is

(a)

$\frac { 2 }{ 3 }$

(b)

$\frac { 5}{ x }$

(c)

$\frac { -14 }{ x }$

(d)

$\frac { 21 }{ x }$

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

(a)

20–6x

(b)

20–3x

(c)

20+6x

(d)

20+3x

3. For the cost function C =$\frac { 1 }{ 25 } { e }^{ 25 }$, the marginal cost is

(a)

$\frac { 1 }{ 25 }$

(b)

$\frac { 1 }{ 5 } { e }^{ 5x }$

(c)

$\frac { 1 }{ 125 } { e }^{ 5x }$

(d)

25e5x

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

(a)

4

(b)

5

(c)

13

(d)

9

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

(a)

Rs 50

(b)

Rs 25

(c)

Rs 100

(d)

Rs 75

6. 3 x 2 = 6
7. 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

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

9. 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.

10. 3 x 3 = 9
11. Find the interval in which the function f(x)=x2–4x+6 is strictly increasing and strictly decreasing.

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

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

14. 2 x 5 = 10
15. 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

16. 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.