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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
Publisher: Brooks Cole
ISBN: 9781285464640

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BuyFindarrow_forward

Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
Publisher: Brooks Cole
ISBN: 9781285464640
Chapter 4.4, Problem 25E
Textbook Problem
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In Exercises 9-38, find the absolute maximum value and the absolute minimum value, if any, of each function.

25. f ( x ) = 4 x + 1 x on [1, 4]

To determine

To find: The absolute maximum and minimum for the given function on the given interval.

Explanation of Solution

Given information:

The given function is,

f(x)=4x+1x (1)

The given interval is [1,4] .

Theorem used:

(1) If f has a local maximum or local minimum value at c and f(c) exists, then f(c)=0 .

(2) “If f is continuous and differentiable on a closed interval [a,b] , then f has both an absolute maximum value and an absolute minimum value on [a,b] .”

Calculation:

The function f increases in the given interval if f(x)>0 and decreases if f(x)<0 , for each value of x in the given interval.

The given function f(x)=4x+1x is continuous and differentiable on the interval [1,4] .

First find the critical points of given function.

Obtain the first derivative of the function f(x)=4x+1x .

f(x)=ddx(4x+1x)=ddx(4x)+ddx(1x)=41x2

Set the above derivative to zero and obtain the critical points

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Chapter 4 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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Minimizing Production costs The daily total cost...Ch. 4.4 - PRINTED BY: fD98Sta0c4e090b@placeholder.10274.edu...Ch. 4.4 - Minimizing Production Costs Re-solve Exercise 52...Ch. 4.4 - Maximizing Revenue Suppose the quantity demanded...Ch. 4.4 - Maximizing Revenue The quantity demanded each...Ch. 4.4 - Air Pollution The amount of nitrogen dioxide, a...Ch. 4.4 - Oxygen Content Of A Pond When organic waste is...Ch. 4.4 - Velocity Of Blood According to a law discovered by...Ch. 4.4 - Maximizing Revenue The average revenue is defined...Ch. 4.4 - CRIME RATES The number of major crimes committed...Ch. 4.4 - Gdp Of a Developing Country A developing country's...Ch. 4.4 - Federal Defict The deficit of the federal...Ch. 4.4 - New Inmates The number of new prison admissions...Ch. 4.4 - Death Rate from AIDS The estimated number of...Ch. 4.4 - Brain Growth And IQs In a study conducted at the...Ch. 4.4 - Brain Growth And IQs Refer to Exercise 67. The...Ch. 4.4 - World Population The total world population is...Ch. 4.4 - VENTURE-CAPITAL INVESTMENT Venture-capital...Ch. 4.4 - Energy Expended By a Fish It has been conjectured...Ch. 4.4 - Reaction To a Drug The strength of a human body's...Ch. 4.4 - Refer to Exercise 72. Show that the rate of change...Ch. 4.4 - Chemical Reaction In an autocatalytic chemical...Ch. 4.4 - Maximum Power Output Suppose the source of current...Ch. 4.4 - Velocity Of a Wave In deep water, a wave of length...Ch. 4.4 - A Mixture Problem A tank initially contains 10 gal...Ch. 4.4 - In Exercises 7884, determine whether the statement...Ch. 4.4 - In Exercises 7884, determine whether the statement...Ch. 4.4 - In Exercises 7884, determine whether the statement...Ch. 4.4 - In Exercises 7884, determine whether the statement...Ch. 4.4 - In Exercises 7884, determine whether the statement...Ch. 4.4 - In Exercises 7884, determine whether the statement...Ch. 4.4 - In Exercises 7884, determine whether the statement...Ch. 4.4 - Let f be a constant function-that is. Let f(x) =...Ch. 4.4 - Show that a polynomial function defined on the...Ch. 4.4 - One condition that must be satisfied before...Ch. 4.4 - One condition that must be satisfied before...Ch. 4.4 - In Exercises 1-6, find the absolute maximum and...Ch. 4.4 - In Exercises 1-6, find the absolute maximum and...Ch. 4.4 - In Exercises 1-6, find the absolute maximum and...Ch. 4.4 - In Exercises 1-6, find the absolute maximum and...Ch. 4.4 - In Exercises 1-6, find the absolute maximum and...Ch. 4.4 - In Exercises 1-6, find the absolute maximum and...Ch. 4.4 - BANK FAILURE The Haven Trust Bank of Duluth, Ga.,...Ch. 4.4 - CONSTRUCTION LOANS Refer to Exercise 7. The amount...Ch. 4.4 - SICKOUTS In a sickout by pilots of American...Ch. 4.4 - AVERAGE 401(K) ACCOUNT BALANCE. The following data...Ch. 4.5 - If the domain of a function f is not a closed...Ch. 4.5 - Refer to Example 4 (page 324). In the solution...Ch. 4.5 - Find the dimensions of a rectangle with a...Ch. 4.5 - Find the dimensions of a rectangle of area 144 ft2...Ch. 4.5 - Enclosing The Largest area The owner of the Rancho...Ch. 4.5 - Enclosing The Largest Area Refer to Exercise 3. As...Ch. 4.5 - Minimizing Construction Costs The management of...Ch. 4.5 - Packaging By cutting away identical squares from...Ch. 4.5 - Metal Fabrication If an open box is made from a...Ch. 4.5 - Minimizing Packaging Cost If an open box has a...Ch. 4.5 - Minimizing Costs A pencil cup with a capacity of...Ch. 4.5 - Minimizing Packaging Costs What are the dimensions...Ch. 4.5 - Minimizing Packaging Costs A rectangular box is to...Ch. 4.5 - Parcel Post Regulations Postal regulations specify...Ch. 4.5 - Book Design A book designer has decided that the...Ch. 4.5 - Parcel Post Regulations Postal regulations specify...Ch. 4.5 - Minimizing Costs A pencil cup with a capacity of 9...Ch. 4.5 - Minimizing costs For its beef stew, Betty Moore...Ch. 4.5 - Product Design The cabinet that will enclose the...Ch. 4.5 - Designing a Norman Window A Norman window has the...Ch. 4.5 - Optimal Charter Flight Fare If exactly 200 people...Ch. 4.5 - Maximizing Yield An apple orchard has an average...Ch. 4.5 - Charter Revenue The owner of a luxury motor yacht...Ch. 4.5 - Profit Of A Vineyard Phillip, the proprietor of a...Ch. 4.5 - Optimal Speed of a Truck A truck gets 600/x mpg...Ch. 4.5 - Minimizing Costs Suppose the cost incurred in...Ch. 4.5 - Strength of a Beam A wooden beam has a rectangular...Ch. 4.5 - Designing a Grain Silo a grain silo has the shape...Ch. 4.5 - Minimizing Cost of Laying Cable In the following...Ch. 4.5 - Strong Radioactive Waste A cylindrical container...Ch. 4.5 - Flights of Birds During daylight hours, some birds...Ch. 4.5 - Minimizing Travel Time A woman is on a lake in a...Ch. 4.5 - Racetrack Design The accompanying figure depicts a...Ch. 4.5 - Inventory Control and Planning The demand for...Ch. 4.5 - Inventory Control and Planning McDuff Preserves...Ch. 4.5 - Inventory Control And Planning Neilsen Cookie...Ch. 4.5 - Inventory Control And Planning A company expects...Ch. 4.5 - Inventory Control and Planning Refer to Exercise...Ch. 4 - Fill in the blanks. 1. a. A function f is...Ch. 4 - Fill in the blanks. 2. a. If f is differentiable...Ch. 4 - Fill in the blanks. 3. a. A function f has a...Ch. 4 - Fill in the blanks. 4. a. A critical number of a...Ch. 4 - a. The graph of a differentiable function f is...Ch. 4 - The line x = a is a vertical asymptote of the...Ch. 4 - For a rational function f(x)=P(x)Q(x) the line x =...Ch. 4 - The line y = b is a horizontal asymptote of the...Ch. 4 - a. A function f has an absolute maximum at c if...Ch. 4 - The extreme value theorem states that if f is ____...Ch. 4 - In Exercises 1-10, (a) find the intervals where...Ch. 4 - In Exercises 1-10, (a) find the intervals where...Ch. 4 - In Exercises 1-10, (a) find the intervals where...Ch. 4 - In Exercises 1-10, (a) find the intervals where...Ch. 4 - In Exercises 1-10, (a) find the intervals where...Ch. 4 - In Exercises 1-10, (a) find the intervals where...Ch. 4 - In Exercises 1-10, (a) find the intervals where...Ch. 4 - In Exercises 1-10, (a) find the intervals where...Ch. 4 - In Exercises 1-10, (a) find the intervals where...Ch. 4 - In Exercises 1-10, (a) find the intervals where...Ch. 4 - In Exercises 11-18, use the curve-sketching guide...Ch. 4 - In Exercises 11-18, use the curve-sketching guide...Ch. 4 - In Exercises 11-18, use the curve-sketching guide...Ch. 4 - In Exercises 11-18, use the curve-sketching guide...Ch. 4 - In Exercises 11-18, use the curve-sketching guide...Ch. 4 - In Exercises 11-18, use the curve-sketching guide...Ch. 4 - In Exercises 11-18, use the curve-sketching guide...Ch. 4 - In Exercises 11-18, use the curve-sketching guide...Ch. 4 - In Exercises 19-22, find the horizontal and...Ch. 4 - In Exercises 19-22, find the horizontal and...Ch. 4 - In Exercises 19-22, find the horizontal and...Ch. 4 - In Exercises 19-22, find the horizontal and...Ch. 4 - In Exercises 23-32, find the absolute maximum...Ch. 4 - In Exercises 23-32, find the absolute maximum...Ch. 4 - In Exercises 23-32, find the absolute maximum...Ch. 4 - In Exercises 23-32, find the absolute maximum...Ch. 4 - In Exercises 23-32, find the absolute maximum...Ch. 4 - In Exercises 23-32, find the absolute maximum...Ch. 4 - In Exercises 23-32, find the absolute maximum...Ch. 4 - In Exercises 23-32, find the absolute maximum...Ch. 4 - In Exercises 23-32, find the absolute maximum...Ch. 4 - In Exercises 23-32, find the absolute maximum...Ch. 4 - Revenue Of Competing Bookstores The graphs of R1...Ch. 4 - Spread OF a Rumor Initially, a handful of students...Ch. 4 - Maximizing Profits Odyssey Travel Agencys monthly...Ch. 4 - Effect of Smoking Bans The sales (in billions of...Ch. 4 - Alternative Minimum Tax Congress created the...Ch. 4 - Measles Deaths Measles is still a leading cause of...Ch. 4 - Effect of Advertising on Sales The total sales S...Ch. 4 - Elderly Workforce The percentage of men 65 years...Ch. 4 - Cost of Producing Calculators a subsidiary of...Ch. 4 - Sales OF Mobile Processors The rising popularity...Ch. 4 - Small Car Market Share in Europe Owing in pan to...Ch. 4 - Index of Environmental Quality The Department of...Ch. 4 - Maximizing Profits The weekly demand for DVDs...Ch. 4 - Maximizing Profits The estimated monthly profit...Ch. 4 - Minimizing Average Cost The total monthly cost (in...Ch. 4 - Worker Efficiency The average worker at Wakefield...Ch. 4 - Senior Workforce The percentage of women 65 years...Ch. 4 - Ace of Drivers in Crash Fatalities The number of...Ch. 4 - Spread of a Contagious Disease The incidence...Ch. 4 - MEDICAL SCHOOL APPLICANTS According to a study...Ch. 4 - Let f(x)={x2+3ifx02ifx=0 a. Compute f(x), and show...Ch. 4 - Maximizing the Volume of A Box A box with an open...Ch. 4 - Minimizing Construction Costs A man wishes to...Ch. 4 - Packaging You wish to construct a closed...Ch. 4 - Inventory Control and Planning Lehen Vinters...Ch. 4 - In what interval is the quadratic function f(x) =...Ch. 4 - Let f(x) = x2 + ax + b. Determine the constants a...Ch. 4 - Find the values of c such that the graph of f(x) =...Ch. 4 - Suppose that the point (a, f(a)) is an inflection...Ch. 4 - Let f(x)={x3+1ifx02ifx=0 a. Compute f(x), and show...Ch. 4 - Find the interval(s) where f(x)=x21x is increasing...Ch. 4 - Find the relative maxima and relative minima, if...Ch. 4 - Find the intervals where the graph of...Ch. 4 - Sketch the graph of f(x) = 2x3 9x2 + 12x 1Ch. 4 - Find the absolute maximum and absolute minimum...Ch. 4 - An open bucket in the form of a right circular...

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