Homework Help is Here – Start Your Trial Now!
Math
Calculus
8. The function C(r) given by: C(x) = 2x² +10 + 32 Define the function: AC(r) = C(x)/.r for x > 0. Define the function: MC(r) dC(r)/dc. Define the term "convex function" and prove that C(c) is convex. Plot the AC and MC functions. Use calculus to establish that the AC function has a unique minimum and that the MC function intersects the AC function at that point. C(x) = 2x² + 10x +32 2

8. The function C(r) given by: C(x) = 2x² +10 + 32 Define the function: AC(r) = C(x)/.r for x > 0. Define the function: MC(r) dC(r)/dc. Define the term "convex function" and prove that C(c) is convex. Plot the AC and MC functions. Use calculus to establish that the AC function has a unique minimum and that the MC function intersects the AC function at that point. C(x) = 2x² + 10x +32 2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
100%

can you please explain the answer by solving this question again?

1 5 8. The function C(r) given by: 1 dc 2 C(x) = 2x² +10 + 32 Define the function: AC(r) = C(x)/x for x > 0. Define the function: MC(c) dC(r)/dc. Define the term "convex function" and prove that C(c) is convex. Plot the AC and MC functions. Use calculus to establish that the AC function has a unique minimum and that the MC function intersects the AC function at that point. dx C64) = 2x²³² + 10x +32 AC(x) = 22 +10 +32 x = = mclxy) = 4x +10 A function f(x) is convex if f"(x) > Note d2c Jx²=4>0 бас Ix = 2-32 бчас ( dz² x2 =O . mc(4) so C is convex for 6470 23 The second deviostre test shows that x=4 is a minimin So there is 9 = x=4 Note AC 700 as x70, only AC (A) = 8 + 10 + 8 = 26 16+10 = 26/ x>0 I minime (270) AC7 ∞ as x-200 for (0) 1 xx according to the grat 270. Samevale so they meet.
Transcribed Image Text:1 5 8. The function C(r) given by: 1 dc 2 C(x) = 2x² +10 + 32 Define the function: AC(r) = C(x)/x for x > 0. Define the function: MC(c) dC(r)/dc. Define the term "convex function" and prove that C(c) is convex. Plot the AC and MC functions. Use calculus to establish that the AC function has a unique minimum and that the MC function intersects the AC function at that point. dx C64) = 2x²³² + 10x +32 AC(x) = 22 +10 +32 x = = mclxy) = 4x +10 A function f(x) is convex if f"(x) > Note d2c Jx²=4>0 бас Ix = 2-32 бчас ( dz² x2 =O . mc(4) so C is convex for 6470 23 The second deviostre test shows that x=4 is a minimin So there is 9 = x=4 Note AC 700 as x70, only AC (A) = 8 + 10 + 8 = 26 16+10 = 26/ x>0 I minime (270) AC7 ∞ as x-200 for (0) 1 xx according to the grat 270. Samevale so they meet.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS