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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.**

To determine

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

**Given information:**

The given function is,

The given interval is

**Theorem used:**

(1) If *f* has a local maximum or local minimum value at *c* and

(2) “If *f* is continuous and differentiable on a closed interval
*f* has both an absolute maximum value and an absolute minimum value on

**Calculation:**

The function *f* increases in the given interval if
*x* in the given interval.

The given function

First find the critical points of given function.

Obtain the first derivative of the function

Set the above derivative to zero and obtain the critical points

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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