The accompanying graph shows the hypothetical cost c= f(x) of manufacturing x items. At approximately what production level does the marginal cost change from decreasing to increasing? c= f(x) 20 40 60 80 100120 Thousands of units produced The marginal cost changes from decreasing to increasing (Type an integer or a decimal.) approximately thousand units

The accompanying graph shows the hypothetical cost c= f(x) of manufacturing x items. At approximately what production level does the marginal cost change from decreasing to increasing? c= f(x) 20 40 60 80 100120 Thousands of units produced The marginal cost changes from decreasing to increasing (Type an integer or a decimal.) approximately thousand units

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...

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Question

The accompanying graph shows the hypothetical cost c= f(x) of manufacturing x items. At approximately what production level does the marginal cost change from decreasing to increasing?
c = f(x)
20 40 60 80 100120
Thousands of units produced
The marginal cost changes from decreasing to increasing at approximately thousand units.
(Type an integer or a decimal.)
Cost

Expert Solution

Step 1

Solution ) cost c = f(x)

Marginal cost = d c/ dx

= f'(x)

Change in marginal cost

= f'(x)/dx = f"(x)

f"(x) is where curvature changes

In interval ( 20 , 60 ) graph is concave down

f"(x) < 0

Interval ( 60 , 120 ) graph is concave up

f"(x) >0

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