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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 3.5, Problem 5E

Textbook Problem

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**Finding the Minimum Average Cost** In Exercises 5–8, find the number of units *x* that minimizes the average cost per unit *C*. *See Example 2*.

To determine

**To calculate:** The number of units *x* that minimizes the average cost function

**Given information:**

The provided cost function is *C* is the cost in dollars and *x* is the unit of product.

**Formula used:**

According to the power rule of differentiation,

According to the average cost function,

Where, *x* is the number of units.

**Calculation:**

Consider the provided cost function,

Now, for the average cost function, divide the cost function by *x*.

Now, for which the cost will minimize, differentiate the average cost function with respect to *x*.

Calculus: An Applied Approach (MindTap Course List)

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Maximum Profit The cost per unit of producing...Ch. 3.5 - Maximum Profit A real estate office handles a...Ch. 3.5 - Maximum Revenue When a wholesaler sold a product...Ch. 3.5 - Maximum Revenue A small theater has a seating...Ch. 3.5 - Minimum Cost A power station is on one side of a...Ch. 3.5 - Minimum Cost An offshore oil well is 1 mile off...Ch. 3.5 - Minimum Cost In Exercises 25 and 26, find the...Ch. 3.5 - Minimum Cost In Exercises 25 and 26, find the...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity In Exercises 27-32, find the price...Ch. 3.5 - Elasticity The demand function for a product is...Ch. 3.5 - Elasticity The demand function for a product is...Ch. 3.5 - Minimum Cost The shipping and handling cost C (in...Ch. 3.5 - Minimum Cost The ordering and transportation cost...Ch. 3.5 - Revenue The demand for a car wash is x=90045p,...Ch. 3.5 - HOW DO YOU SEE IT? Match each graph with the...Ch. 3.5 - Sales The sales S (in billions of dollars) for...Ch. 3.5 - Sales The sales S (in billions of dollars) for...Ch. 3.5 - Demand A demand function is modeled by x=apm where...Ch. 3.6 - Checkpoint 1 Worked-out solution available at...Ch. 3.6 - Checkpoint 2 Worked-out solution available at...Ch. 3.6 - Checkpoint 3 Worked-out solution available at...Ch. 3.6 - Checkpoint 4 Worked-out solution available at...Ch. 3.6 - Checkpoint 5 Worked-out solution available at...Ch. 3.6 - Checkpoint 6 Worked-out solution available at...Ch. 3.6 - Checkpoint 7 Worked-out solution available at...Ch. 3.6 - Checkpoint 8 Worked-out solution available at...Ch. 3.6 - In Exercises 1-8, find the limit. limx2(x+1)Ch. 3.6 - In Exercises 1-8, find the limit. limx1(3x+4)Ch. 3.6 - In Exercises 1-8, find the limit. limx32x2+x15x+3Ch. 3.6 - In Exercises 1-8, find the limit. limx34x29x9x3Ch. 3.6 - In Exercises 1-8, find the limit....Ch. 3.6 - In Exercises 1-8, find the limit. limx1x26x+5x21Ch. 3.6 - In Exercises 1-8, find the limit. limx0+xCh. 3.6 - In Exercises 1-8, find the limit. limx1(x+x1)Ch. 3.6 - In Exercises 9-12, find the average cost function...Ch. 3.6 - In Exercises 9-12, find the average cost function...Ch. 3.6 - In Exercises 9-12, find the average cost function...Ch. 3.6 - In Exercises 9-12, find the average cost function...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Vertical and Horizontal Asymptotes In Exercises...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - Finding Infinite Limits In Exercises 7-12, find...Ch. 3.6 - Finding Vertical Asymptotes In Exercises 13-18,...Ch. 3.6 - Finding Vertical Asymptotes In Exercises 13-18,...Ch. 3.6 - Finding Vertical Asymptotes In Exercises 13-18,...Ch. 3.6 - Finding Vertical Asymptotes In Exercises 13-18,...Ch. 3.6 - Finding Vertical Asymptotes In Exercises 13-18,...Ch. 3.6 - Finding Vertical Asymptotes In Exercises 13-18,...Ch. 3.6 - Determining Infinite Limits In Exercises 19-24,...Ch. 3.6 - Determining Infinite Limits In Exercises 19-24,...Ch. 3.6 - Determining Infinite Limits In Exercises 19-24,...Ch. 3.6 - Determining Infinite Limits In Exercises 19-24,...Ch. 3.6 - Determining Infinite Limits In Exercises 19-24,...Ch. 3.6 - Determining Infinite Limits In Exercises 19-24,...Ch. 3.6 - Finding Limits at Infinity In Exercises 25-28,...Ch. 3.6 - Finding Limits at Infinity In Exercises 25-28,...Ch. 3.6 - Finding Limits at Infinity In Exercises 25-28,...Ch. 3.6 - Finding Limits at Infinity In Exercises 25-28,...Ch. 3.6 - Finding Horizontal Asymptotes In Exercises 29-36,...Ch. 3.6 - Finding Horizontal Asymptotes In Exercises 29-36,...Ch. 3.6 - Finding Horizontal Asymptotes In Exercises 29-36,...Ch. 3.6 - Finding Horizontal Asymptotes In Exercises 29-36,...Ch. 3.6 - Finding Horizontal Asymptotes In Exercises 29-36,...Ch. 3.6 - Finding Horizontal Asymptotes In Exercises 29-36,...Ch. 3.6 - Finding Horizontal Asymptotes In Exercises 29-36,...Ch. 3.6 - Finding Horizontal Asymptotes In Exercises 29-36,...Ch. 3.6 - Using Horizontal Asymptotes In Exercises 37-40,...Ch. 3.6 - Using Horizontal Asymptotes In Exercises 37-40,...Ch. 3.6 - Using Horizontal Asymptotes In Exercises 37-40,...Ch. 3.6 - Using Horizontal Asymptotes In Exercises 37-40,...Ch. 3.6 - Finding Limits at Infinity In Exercises 41 and 42,...Ch. 3.6 - Finding Limits at Infinity In Exercises 41 and 42,...Ch. 3.6 - Finding Limits at Infinity In Exercises 43 and 44,...Ch. 3.6 - Finding Limits at Infinity In Exercises 43 and 44,...Ch. 3.6 - Estimating Limits at Infinity In Exercises 45-48,...Ch. 3.6 - Estimating Limits at Infinity In Exercises 45-48,...Ch. 3.6 - Estimating Limits at Infinity In Exercises 45-48,...Ch. 3.6 - Estimating Limits at Infinity In Exercises 45-48,...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 4962, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 4962, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Sketching Graphs In Exercises 49-62, sketch the...Ch. 3.6 - Average Cost The cost C (in dollars) of producing...Ch. 3.6 - Average Cost The cost C (in dollars) for a company...Ch. 3.6 - Average Profit The cost C and revenue R functions...Ch. 3.6 - HOW DO YOU SEE IT? The graph shows the temperature...Ch. 3.6 - Seizing Drugs The cost C (in millions of dollars)...Ch. 3.6 - Recycling Bins The cost C (in dollars) of...Ch. 3.6 - Learning Curve Psychologists have developed...Ch. 3.7 - Checkpoint 1 Worked-out solution available at...Ch. 3.7 - Checkpoint 2 Worked-out solution available at...Ch. 3.7 - Checkpoint 3 Worked out solution available at...Ch. 3.7 - Checkpoint 4 Worked-out solution available at...Ch. 3.7 - Checkpoint 5 Worked-out solution available at...Ch. 3.7 - In Exercises 1-4, find the vertical and horizontal...Ch. 3.7 - In Exercises 1-4, find the vertical and horizontal...Ch. 3.7 - In Exercises 1-4, find the vertical and horizontal...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - In Exercises 5-10, find the open intervals on...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 122, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 122, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 122, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 122, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Analyzing a Graph In Exercises 1-22, analyze and...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Graphing a Function In Exercises 23-36, use a...Ch. 3.7 - Interpreting a Graph In Exercises 37-40, use the...Ch. 3.7 - Interpreting a Graph In Exercises 37-40, use the...Ch. 3.7 - Interpreting a Graph In Exercises 37-40, use the...Ch. 3.7 - Interpreting a Graph In Exercises 37-40, use the...Ch. 3.7 - Sketching a Function In Exercises 41 and 42,...Ch. 3.7 - Sketching a Function In Exercises 41 and 42,...Ch. 3.7 - Creating a Function In Exercises 43 and 44, create...Ch. 3.7 - Creating a Function In Exercises 43 and 44, create...Ch. 3.7 - 45. Social Security The table lists the average...Ch. 3.7 - Cost An employee of a delivery company earns $14...Ch. 3.7 - Meteorology The monthly average high temperature T...Ch. 3.7 - HOW DO YOU SEE IT? The graph shows a companys...Ch. 3.7 - Writing In Exercises 49 and 50, use a graphing...Ch. 3.7 - Writing In Exercises 49 and 50, use a graphing...Ch. 3.7 - Discovery Consider the function f(x)=x22x+4x22 (a)...Ch. 3.8 - Checkpoint 1 Worked-out solution available at...Ch. 3.8 - Checkpoint 2 Worked-out solution available at...Ch. 3.8 - Checkpoint 3 Worked-out solution available at...Ch. 3.8 - Checkpoint 4 Worked-out solution available at...Ch. 3.8 - In Exercises 1-12, find the derivative....Ch. 3.8 - In Exercises 1-12, find the derivative....Ch. 3.8 - In Exercises 1-12, find the derivative....Ch. 3.8 - In Exercises 1-12, find the derivative....Ch. 3.8 - In Exercises 1-12, find the derivative....Ch. 3.8 - In Exercises 1-12, find the derivative....Ch. 3.8 - In Exercises 1-12, find the derivative. A=143x2Ch. 3.8 - In Exercises 1-12, find the derivative. A=29x2Ch. 3.8 - In Exercises 1-12, find the derivative. C=2rCh. 3.8 - In Exercises 1-12, find the derivative. 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Revenue The revenue R for a company selling x...Ch. 3.8 - Demand The demand function for a product is...Ch. 3.8 - HOW DO YOU SEE IT? The graph shows the profit P...Ch. 3.8 - Biology: Wildlife Management A state game...Ch. 3.8 - Medical Science The concentration C (in milligrams...Ch. 3.8 - Marginal Analysis A retailer has determined that...Ch. 3.8 - Marginal Analysis The demand x for a web camera is...Ch. 3.8 - Error Propagation In Exercises 41 and 42, use the...Ch. 3.8 - Error Propagation In Exercises 41 and 42, use the...Ch. 3.8 - True or False? In Exercises 43 and 44, determine...Ch. 3.8 - True or False? 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Maximum Profit A commodity has a demand...Ch. 3 - Maximum Profit The profit P (in thousands of...Ch. 3 - Elasticity The demand function for a product is...Ch. 3 - Elasticity The demand function for a product is...Ch. 3 - Finding Vertical Asymptotes In Exercises 67-70,...Ch. 3 - Finding Vertical Asymptotes In Exercises 67-70,...Ch. 3 - Finding Vertical Asymptotes In Exercises 67-70,...Ch. 3 - Finding Vertical Asymptotes In Exercises 67-70,...Ch. 3 - Determining Infinite Limits In Exercises 71-74,...Ch. 3 - Determining Infinite Limits In Exercises 71-74,...Ch. 3 - Determining Infinite Limits In Exercises 71-74,...Ch. 3 - Determining Infinite Limits In Exercises 71-74,...Ch. 3 - Finding Horizontal Asymptotes In Exercises 75-78,...Ch. 3 - Finding Horizontal Asymptotes In Exercises 75-78,...Ch. 3 - Finding Horizontal Asymptotes In Exercises 75-78,...Ch. 3 - Finding Horizontal Asymptotes In Exercises 75-78,...Ch. 3 - 79. Average Cost The cost C (in dollars) of...Ch. 3 - 80. Average Cost The cost C (in dollars) of...Ch. 3 - Seizing Drugs The cost C (in millions of dollars)...Ch. 3 - Removing Pollutants The cost C (in dollars) of...Ch. 3 - Analyzing a Graph In Exercises 8394, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Analyzing a Graph In Exercises 83-94, analyze and...Ch. 3 - Bacteria The data in the table show the number N...Ch. 3 - Meteorology The monthly average high temperature T...Ch. 3 - Comparing y and dy In Exercises 97-100, compare...Ch. 3 - Comparing y and dy In Exercises 97-100, compare...Ch. 3 - Comparing y and dy In Exercises 97-100, compare...Ch. 3 - Comparing y and dy In Exercises 97-100, compare...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Marginal Analysis In Exercises 101-106, use...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Finding Differentials In Exercises 107-112, find...Ch. 3 - Profit The profit P (in dollars) for a company...Ch. 3 - Demand The demand function for a product is...Ch. 3 - Physiology: Body Surface Area The body surface...Ch. 3 - In Exercises 1-3, find the critical numbers and...Ch. 3 - In Exercises 1-3, find the critical numbers and...Ch. 3 - In Exercises 1-3, find the critical numbers and...Ch. 3 - In Exercises 4-6, use the First-Derivative Test to...Ch. 3 - In Exercises 4-6, use the First-Derivative Test to...Ch. 3 - In Exercises 4-6, use the First-Derivative Test to...Ch. 3 - In Exercises 7-9, find the absolute extrema of the...Ch. 3 - In Exercises 7-9, find the absolute extrema of the...Ch. 3 - In Exercises 7-9, find the absolute extrema of the...Ch. 3 - In Exercises 10-13, discuss the concavity of the...Ch. 3 - In Exercises 10-13, discuss the concavity of the...Ch. 3 - In Exercises 10-13, discuss the concavity of the...Ch. 3 - In Exercises 10-13, discuss the concavity of the...Ch. 3 - In Exercises 14 and 15, find all relative extrema...Ch. 3 - In Exercises 14 and 15, find all relative extrema...Ch. 3 - In Exercises 16-18, find the vertical and...Ch. 3 - In Exercises 16-18, find the vertical and...Ch. 3 - In Exercises 16-18, find the vertical and...Ch. 3 - In Exercises 19-21, analyze and sketch the graph...Ch. 3 - In Exercises 19-21, analyze and sketch the graph...Ch. 3 - In Exercises 19-21, analyze and sketch the graph...Ch. 3 - 22. Find the value of dy when and . Compare this...Ch. 3 - A commodity has a demand function modeled by...

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