#### Applications of Differentiation Two Marks Questions

11th Standard

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Time : 00:45:00 Hrs
Total Marks : 20
10 x 2 = 20
1. The demand function for a commodity is $p={4\over x}$, where p is unit price. Find the instantaneous rate of change of demand with respect to price at p=4. Also interpret your result.

2. 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

3. Find the price elasticity of demand for the demand function x = 10 – p where x is the demand and p i the price. Examine whether the demand is elastic, inelastic or unit elastic at p = 6.

4. Find the equilibrium price and equilibrium quantity for the following functions. Demand: x =100 – 2p and supply: x = 3p –50

5. If f (x, y)  = 3x2 + 4y3 + 6xy - x3y3 + 7 then show that fxy (1,1) = 18.

6. If y=x-1/x, prove that y is a strictly increasing function for all real vaules of x(x$\neq$0).

7. Prove that 75-12x+6x2-x3 always decreases as x increases.

8. Find the maximum and minimum values of x3-6x2+7

9. If f(x,y) = 3x2 + 4y3 + 6xy - x2y3 + 6. Find fx(1, -1)

10. If f(x,y) = 3x2 + 4y3 + 6xy - x2y3 + 6. Find fyy(1,1)