A.find the absolute maximum and minimum values of each function over the indicat

Question

A.find the absolute maximum and minimum values of each function over the indicated interval, and indicate the x-values at which they occur. f(x)=2x^3-2x^2-2x+3; [-1,0]

B. for a certain automobile? M(x)=-.015x^2+1.36x-7.6 represents the miles per gallon obtained at a speed of x miles per hour? 30<x<60.(both is less than or equal too) find the absolute extrema and interpret your answer

c. the price of a ticket to a baseball game rises from $12.00 to $15.00. The quantity of tickets sold falls from 180,000 to 164,000. Calculate the elasticity of demand and state whether it is elastic, inelastic, or unit elsatic. Will revenue rise decline or stay the same?

E. Find the elsasticty of demand (E) for the given demand finction at the indicated values of p. Is the demand elastic, inelastic, or unit elastic at the indicated values and how does this relate to change in price?

q=406-0.03p^2

A. $20   

B. $36

Explanation / Answer

A.find the absolute maximum and minimum values of each function over the indicated interval, and indicate the x-values at which they occur. f(x)=2x^3-2x^2-2x+3; [-1,0]

take the derivative: 6x^2 - 4x - 2 = 0

2(3x^2 - 2x - 1) = 0

2(3x + 1)(x - 1) = 0

x = -1/3 , 1

plug in x = -1, 0 (the endpoints) and -1/3 (the critical number inside the interval) into the original function, the highest is the mx and lowest is the min.

B. for a certain automobile? M(x)=-.015x^2+1.36x-7.6 represents the miles per gallon obtained at a speed of x miles per hour? 30<x<60.(both is less than or equal too) find the absolute extrema and interpret your answer

Again take the derivative: -0.03x + 1.36 = 0

x = 1.36/.03 = 45.33333

plug in x = 30, 60 and 45.333333 into M(x), the highest is your max, the lowest is your min. This would be the max and min miles per gallon (for the x values).

c. the price of a ticket to a baseball game rises from $12.00 to $15.00. The quantity of tickets sold falls from 180,000 to 164,000. Calculate the elasticity of demand and state whether it is elastic, inelastic, or unit elsatic. Will revenue rise decline or stay the same?

Elasticity = % change in Quantity / % change in price = (164 - 180) / 180 over (15-12)/15 = -.0888 / .2 = -.4444444

so 0.44444 < 1 so inelastic. Revenue will decrease.

E. Find the elsasticty of demand (E) for the given demand finction at the indicated values of p. Is the demand elastic, inelastic, or unit elastic at the indicated values and how does this relate to change in price?

q=406-0.03p^2

A. $20   

B. $36

Elasticity = dQ/Q over dP / P = dQ/dP * P/Q

part a)

dq/dp = -.06p = -.06 (20) =-1.2

P = 20, q = 406 - 12 = 394

Elasticity = -1.2 * 20/394 < 1 so inelastic.

Do the same thing for $36.

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