(a) Answer Local maximum P ( 1.8 ) = 2.1 to the nearest tenth Local minimum P ( 3.6 ) = − 0.6 to the nearest tenth Explanation Given information: Given function, P ( x ) = ( x − 1 ) ( x − 3 ) ( x − 4 ) Calculation: Need to graph the function P ( x ) = ( x − 1 ) ( x − 3 ) ( x − 4 ) and need to find all extrema, correct to the nearest tenth. Graphing P ( x ) using calculator: From the above graph, it is clear that the graph has local maximum P ( 1.8 ) = 2.1 to the nearest tenth. Graphing P ( x ) using calculator: From the above graph, it is clear that the graph has local minimum P ( 3.6 ) = − 0.6 to the nearest tenth. (b) To determine To sketch: the graph of the given function and find all local extrema. Answer The local maximum is Q ( 1.8 ) = 7.1 to the nearest tenth. The local maximum is Q ( 3.6 ) = 4.4 to the nearest tenth. Explanation Given information: Given function, Q ( x ) = ( x − 1 ) ( x − 3 ) ( x − 4 ) + 5 Calculation: Need to graph the function Q ( x ) = ( x − 1 ) ( x − 3 ) ( x − 4 ) + 5 and need to find all extrema, correct to the nearest tenth. Graphing Q ( x ) using calculator: Here the function Q ( x ) is obtained by shifting the graph of P ( x ) upwards by 5 units. So the local maximum is obtained by adding 5 units P ( x ) to get Q ( x ) . Q ( 1.8 ) = P ( 1.8 ) + 5 = 2.1 + 5 = 7.1 Hence, the local maximum is Q ( 1.8 ) = 7.1 to the nearest tenth. Now the local minimum is obtained by adding 5 units to P ( x ) to get Q ( x ) . Q ( 3.6 ) = P ( 3.6 ) + 5 = − 0.6 + 5 = 4.4 Hence, the local maximum is Q ( 3.6 ) = 4.4 to the nearest tenth.

Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Question

Chapter 3.2, Problem 78E

(a)

To determine

To sketch: the graph of the given function and find all local extrema.

(a)

Expert Solution

Answer to Problem 78E

Local maximum P(1.8)=2.1 to the nearest tenth

Local minimum P(3.6)=−0.6 to the nearest tenth

Explanation of Solution

Given information:

Given function,

P(x)=(x−1)(x−3)(x−4)

Calculation:

Need to graph the function P(x)=(x−1)(x−3)(x−4) and need to find all extrema, correct to the nearest tenth.

Graphing P(x) using calculator:

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 3.2, Problem 78E , additional homework tip 1

From the above graph, it is clear that the graph has local maximum P(1.8)=2.1 to the nearest tenth.

Graphing P(x) using calculator:

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 3.2, Problem 78E , additional homework tip 2

From the above graph, it is clear that the graph has local minimum P(3.6)=−0.6 to the nearest tenth.

(b)

To determine

To sketch: the graph of the given function and find all local extrema.

(b)

Expert Solution

Answer to Problem 78E

The local maximum is Q(1.8)=7.1 to the nearest tenth.

The local maximum is Q(3.6)=4.4 to the nearest tenth.

Explanation of Solution

Given information:

Given function,

Q(x)=(x−1)(x−3)(x−4)+5

Calculation:

Need to graph the function Q(x)=(x−1)(x−3)(x−4)+5 and need to find all extrema, correct to the nearest tenth.

Graphing Q(x) using calculator:

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 3.2, Problem 78E , additional homework tip 3

Here the function Q(x) is obtained by shifting the graph of P(x) upwards by 5 units. So the local maximum is obtained by adding 5 units P(x) to get Q(x) .

Q(1.8)=P(1.8)+5=2.1+5=7.1

Hence, the local maximum is Q(1.8)=7.1 to the nearest tenth.

Now the local minimum is obtained by adding 5 units to P(x) to get Q(x) .

Q(3.6)=P(3.6)+5=−0.6+5=4.4

Hence, the local maximum is Q(3.6)=4.4 to the nearest tenth.

Chapter 3.2, Problem 77E

Chapter 3.2, Problem 79E

Chapter 3 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 3.1 - To put the quadratic function f(x)=ax2+bx+c in...Ch. 3.1 - The quadratic function f(x) = a(x - h)2 + k is in...Ch. 3.1 - The graph of f(x) = 3(x - 2)2 - 6 is a parabola...Ch. 3.1 - The graph of f(x) = -3(x - 2)2 - 6 is a parabola...Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - Prob. 61E Ch. 3.1 - Prob. 62E Ch. 3.1 - Height of a Ball If a ball is thrown directly...Ch. 3.1 - Path of a Ball A ball is thrown across a playing...Ch. 3.1 - Revenue A manufacturer finds that the revenue...Ch. 3.1 - Sales A soft-drink vendor at a popular beach...Ch. 3.1 - Advertising The effectiveness of a television...Ch. 3.1 - Pharmaceuticals When a certain drug is taken...Ch. 3.1 - Agriculture The number of apples produced by each...Ch. 3.1 - Agriculture At a certain vineyard it is found that...Ch. 3.1 - Prob. 71E Ch. 3.1 - Prob. 72E Ch. 3.1 - Prob. 73E Ch. 3.1 - Prob. 74E Ch. 3.1 - Fencing a Horse Corral Carol has 2400 ft of...Ch. 3.1 - Making a Rain Gutter A rain gutter is formed by...Ch. 3.1 - Stadium Revenue A baseball team plays in a stadium...Ch. 3.1 - Prob. 78E Ch. 3.1 - Prob. 79E Ch. 3.1 - Prob. 80E Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Which of the following statements couldnt possibly...Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - 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If c is a real zero of the...Ch. 3.4 - True or False? 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Prob. 102E Ch. 3.4 - Prob. 103E Ch. 3.4 - Prob. 104E Ch. 3.4 - Prob. 105E Ch. 3.4 - Prob. 106E Ch. 3.4 - Possible Rational Zeros A polynomial function P...Ch. 3.4 - Possible Rational Zeros A polynomial function P...Ch. 3.5 - Prob. 1E Ch. 3.5 - Prob. 2E Ch. 3.5 - Prob. 3E Ch. 3.5 - Prob. 4E Ch. 3.5 - Prob. 5E Ch. 3.5 - Prob. 6E Ch. 3.5 - Prob. 7E Ch. 3.5 - Prob. 8E Ch. 3.5 - Prob. 9E Ch. 3.5 - Prob. 10E Ch. 3.5 - Prob. 11E Ch. 3.5 - Prob. 12E Ch. 3.5 - Prob. 13E Ch. 3.5 - Prob. 14E Ch. 3.5 - Prob. 15E Ch. 3.5 - Prob. 16E Ch. 3.5 - Prob. 17E Ch. 3.5 - Prob. 18E Ch. 3.5 - Prob. 19E Ch. 3.5 - Prob. 20E Ch. 3.5 - Prob. 21E Ch. 3.5 - Prob. 22E Ch. 3.5 - Prob. 23E Ch. 3.5 - Prob. 24E Ch. 3.5 - Prob. 25E Ch. 3.5 - Prob. 26E Ch. 3.5 - Prob. 27E Ch. 3.5 - Prob. 28E Ch. 3.5 - Prob. 29E Ch. 3.5 - Prob. 30E Ch. 3.5 - Prob. 31E Ch. 3.5 - Prob. 32E Ch. 3.5 - Prob. 33E Ch. 3.5 - Prob. 34E Ch. 3.5 - Prob. 35E Ch. 3.5 - Prob. 36E Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - Prob. 40E Ch. 3.5 - 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Prob. 30E Ch. 3.7 - Prob. 31E Ch. 3.7 - Prob. 32E Ch. 3.7 - Prob. 33E Ch. 3.7 - Prob. 34E Ch. 3.7 - Prob. 35E Ch. 3.7 - Prob. 36E Ch. 3.7 - Prob. 37E Ch. 3.7 - Prob. 38E Ch. 3.7 - Prob. 39E Ch. 3.7 - Prob. 40E Ch. 3.7 - Prob. 41E Ch. 3.7 - Prob. 42E Ch. 3.7 - Prob. 43E Ch. 3.7 - Prob. 44E Ch. 3.7 - Prob. 45E Ch. 3.7 - Prob. 46E Ch. 3.7 - Prob. 47E Ch. 3.7 - Prob. 48E Ch. 3.7 - Prob. 49E Ch. 3.7 - Prob. 50E Ch. 3.7 - Prob. 51E Ch. 3.7 - Prob. 52E Ch. 3.7 - Prob. 53E Ch. 3.7 - Prob. 54E Ch. 3.7 - Prob. 55E Ch. 3.7 - Prob. 56E Ch. 3.7 - Prob. 57E Ch. 3.7 - Prob. 58E Ch. 3.7 - Prob. 59E Ch. 3.7 - Prob. 60E Ch. 3.7 - Prob. 61E Ch. 3.7 - Prob. 62E Ch. 3.7 - Prob. 63E Ch. 3.7 - Prob. 64E Ch. 3.7 - Prob. 65E Ch. 3.7 - Prob. 66E Ch. 3.7 - Prob. 67E Ch. 3.7 - Prob. 68E Ch. 3.7 - Prob. 69E Ch. 3.7 - Prob. 70E Ch. 3.7 - Prob. 71E Ch. 3.7 - Prob. 72E Ch. 3.7 - Prob. 73E Ch. 3.7 - Prob. 74E Ch. 3.7 - Prob. 75E Ch. 3.7 - Prob. 76E Ch. 3.7 - Prob. 77E Ch. 3.7 - Prob. 78E Ch. 3.7 - Prob. 79E Ch. 3.7 - Prob. 80E Ch. 3.7 - Prob. 81E Ch. 3.7 - Prob. 82E Ch. 3.7 - Prob. 83E Ch. 3.7 - Drug Concentration After a certain drug is...Ch. 3.7 - Drug Concentration A drug is administered to a...Ch. 3.7 - Flight of a Rocket Suppose a rocket is fired...Ch. 3.7 - The Doppler Effect As a train moves toward an...Ch. 3.7 - Prob. 88E Ch. 3.7 - Prob. 89E Ch. 3.7 - Prob. 90E Ch. 3.7 - Prob. 91E Ch. 3.7 - Prob. 92E Ch. 3 - Prob. 1RCC Ch. 3 - Prob. 2RCC Ch. 3 - Prob. 3RCC Ch. 3 - Prob. 4RCC Ch. 3 - Prob. 5RCC Ch. 3 - Prob. 6RCC Ch. 3 - Prob. 7RCC Ch. 3 - Prob. 8RCC Ch. 3 - Prob. 9RCC Ch. 3 - Prob. 10RCC Ch. 3 - Prob. 11RCC Ch. 3 - Prob. 12RCC Ch. 3 - Prob. 13RCC Ch. 3 - Prob. 1RE Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Prob. 26RE Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE Ch. 3 - Prob. 74RE Ch. 3 - Prob. 75RE Ch. 3 - Prob. 76RE Ch. 3 - Prob. 77RE Ch. 3 - Prob. 78RE Ch. 3 - Prob. 79RE Ch. 3 - Prob. 80RE Ch. 3 - Prob. 81RE Ch. 3 - Prob. 82RE Ch. 3 - Prob. 83RE Ch. 3 - Prob. 84RE Ch. 3 - Prob. 85RE Ch. 3 - Prob. 86RE Ch. 3 - Express the quadratic function f(x) = x2 x 6 in...Ch. 3 - Find the maximum or minimum value of the quadratic...Ch. 3 - A cannonball fired out to sea from a shore battery...Ch. 3 - Graph the polynomial P(x) = (x + 2)3 + 27, showing...Ch. 3 - (a) Use synthetic division to find the quotient...Ch. 3 - Let P(x) = 2x3 5x2 4x + 3. (a) List all possible...Ch. 3 - Prob. 7T Ch. 3 - Find all real and complex zeros of P(x) = x3 x2 ...Ch. 3 - Find the complete factorization of P(x) = x4 2x3...Ch. 3 - Find a fourth-degree polynomial with integer...Ch. 3 - Let P(x) = 2x4 7x3 + x2 18x + 3. (a) Use...Ch. 3 - Prob. 12T Ch. 3 - Prob. 1P Ch. 3 - Prob. 2P Ch. 3 - How Fast Can You List Your Favorite Things? If you...Ch. 3 - Prob. 4P Ch. 3 - Height of a Baseball A baseball is thrown upward,...Ch. 3 - Torricelli's Law Water in a tank will flow out of...

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