1. Karen is a hobby farmer from near Toowoomba in Southern Queens- land. She sells the lettuce she grows to her local supermarket. The total revenue (in AUD) Karen makes from selling x boxes of lettuce per week is given by the function R(x) = 2x(x - 12). The average cost of producing each box is given by 2x + 3 C(x): x (a) Use the quotient rule to determine Karen's marginal average cost function C'(x). (b) What is Karen's total cost function C(x)? (c) Determine the marginal revenue R'(6) using the product rule. (d) Briefly comment on what (c) means in terms of Karen's business. (e) Determine Karen's profit function P(x). (f) Compare the slope of the tangent to the curve y = points (5,57) and (6,57). P(x) at the
1. Karen is a hobby farmer from near Toowoomba in Southern Queens- land. She sells the lettuce she grows to her local supermarket. The total revenue (in AUD) Karen makes from selling x boxes of lettuce per week is given by the function R(x) = 2x(x - 12). The average cost of producing each box is given by 2x + 3 C(x): x (a) Use the quotient rule to determine Karen's marginal average cost function C'(x). (b) What is Karen's total cost function C(x)? (c) Determine the marginal revenue R'(6) using the product rule. (d) Briefly comment on what (c) means in terms of Karen's business. (e) Determine Karen's profit function P(x). (f) Compare the slope of the tangent to the curve y = points (5,57) and (6,57). P(x) at the
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.2: Transformations Of Quadratic Functions
Problem 50PFA
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Transcribed Image Text:1. Karen is a hobby farmer from near Toowoomba in Southern Queens-
land. She sells the lettuce she grows to her local supermarket. The
total revenue (in AUD) Karen makes from selling x boxes of lettuce
per week is given by the function
R(x) = 2x(x - 12).
The average cost of producing each box is given by
2x + 3
C(x) =
X
(a) Use the quotient rule to determine Karen's marginal average cost
function C'(x).
(b) What is Karen's total cost function C(x)?
(c) Determine the marginal revenue R'(6) using the product rule.
(d) Briefly comment on what (c) means in terms of Karen's business.
(e) Determine Karen's profit function P(x).
(f) Compare the slope of the tangent to the curve y = P(x) at the
points (5,57) and (6,57).
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