Section 3.7

Find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent. f(x) = 4500 - 4x^2; x = 20

-5.5%

Find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent. f(x) = 200 + 50x; x = 3

14.3%

Find the elasticity of the demand function as a function of p. x = D(p) = 500/(p+8)^2

E(p) = 2p/p+8

Find the elasticity of the demand function as a function of p. x = D(p) = √700-p

E(p) = p/1,400-2p

Find the elasticity of the demand function as a function of p. x = D(p) = 800 - p

E(p) = p/800-p

Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p. x = f(p) = 214 - 5p; p = 31.

Elastic

Use the price-demand equation to find the values of p which meet the given condition of elasticity. x = f(p) = 216-2p^2; determine the values of p for which demand is elastic and the values of p for which demand is inelastic..

Elastic on (6, 6 √3), inelastic on (0, 6)

Solve the problem. A beverage company works out a demand function for its sale of soda and finds it to be x = D(p) = 2,900 - 21p where x = the quantity of sodas sold when the price per can, in cents, is p. At what prices, p, is the elasticity of demand inelastic?

For p < 69 cents

Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p. x = f(p) = 2005 - p^2; p = 13

Inelastic

Use the demand equation to find the revenue function. x = f(p) = 30(15 - p)

R(p) = 450p - 30p^2

Use the price-demand equation to find the values of p which meet the given condition of elasticity. x = f(p)= 168 - 7p; determine the values of p for which demand has unit elasticity. Round to two decimal places if necessary.

Unit at p = 12

Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p. x = f(p) = 1500 - 5p^2; p = 10

Unit elastic