The extrema of the function f ( x ) = − x 2 + 6 x − 8 on the interval [ 1 , 6 ] .

Question

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Answer 1

Question

Chapter 4.9, Problem 1E

To determine

To calculate:The extrema of the function f(x)=−x2+6x−8 on the interval [1,6] .

Expert Solution & Answer

Answer to Problem 1E

The function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0)and the minimum value as −8at the point (6,0) on the interval [1,6] .

Explanation of Solution

Given information:

The function f(x)=−x2+6x−8 and the interval [1,6] .

Formula used:

If a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

Calculation:

Consider the function f(x)=−x2+6x−8 and the interval [1,6] .

Sketch the graph of the function f(x)=−x2+6x−8 on the coordinate axes.

Calculus : The Classic Edition (with Make the Grade and Infotrac), Chapter 4.9, Problem 1E

Observe that graph is a downward parabola.

Recall if a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

From the graph it is clear that function has maximum value at the point (3,0) . Evaluate the value of the function at the point.

f(3)=−x2+6x−8=−(3)2+6(3)−8=−9+18−8=1

The maximum value is 1. This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≤f(3) holds true.

From the graph it is clear that function has minimum value at the point (6,0) . Evaluate the value of the function at the point.

f(6)=−x2+6x−8=−(6)2+6(6)−8=−36+36−8=−8

The minimum value is −8 .This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≥f(6) holds true.

Thus, the function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0) and the minimum value as −8 at the point (6,0) on the interval [1,6] .

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Answer 2

Question

Chapter 4.9, Problem 1E

To determine

To calculate:The extrema of the function f(x)=−x2+6x−8 on the interval [1,6] .

Expert Solution & Answer

Answer to Problem 1E

The function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0)and the minimum value as −8at the point (6,0) on the interval [1,6] .

Explanation of Solution

Given information:

The function f(x)=−x2+6x−8 and the interval [1,6] .

Formula used:

If a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

Calculation:

Consider the function f(x)=−x2+6x−8 and the interval [1,6] .

Sketch the graph of the function f(x)=−x2+6x−8 on the coordinate axes.

Calculus : The Classic Edition (with Make the Grade and Infotrac), Chapter 4.9, Problem 1E

Observe that graph is a downward parabola.

Recall if a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

From the graph it is clear that function has maximum value at the point (3,0) . Evaluate the value of the function at the point.

f(3)=−x2+6x−8=−(3)2+6(3)−8=−9+18−8=1

The maximum value is 1. This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≤f(3) holds true.

From the graph it is clear that function has minimum value at the point (6,0) . Evaluate the value of the function at the point.

f(6)=−x2+6x−8=−(6)2+6(6)−8=−36+36−8=−8

The minimum value is −8 .This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≥f(6) holds true.

Thus, the function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0) and the minimum value as −8 at the point (6,0) on the interval [1,6] .

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Answer 3

Question

Chapter 4.9, Problem 1E

To determine

To calculate:The extrema of the function f(x)=−x2+6x−8 on the interval [1,6] .

Expert Solution & Answer

Answer to Problem 1E

The function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0)and the minimum value as −8at the point (6,0) on the interval [1,6] .

Explanation of Solution

Given information:

The function f(x)=−x2+6x−8 and the interval [1,6] .

Formula used:

If a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

Calculation:

Consider the function f(x)=−x2+6x−8 and the interval [1,6] .

Sketch the graph of the function f(x)=−x2+6x−8 on the coordinate axes.

Calculus : The Classic Edition (with Make the Grade and Infotrac), Chapter 4.9, Problem 1E

Observe that graph is a downward parabola.

Recall if a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

From the graph it is clear that function has maximum value at the point (3,0) . Evaluate the value of the function at the point.

f(3)=−x2+6x−8=−(3)2+6(3)−8=−9+18−8=1

The maximum value is 1. This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≤f(3) holds true.

From the graph it is clear that function has minimum value at the point (6,0) . Evaluate the value of the function at the point.

f(6)=−x2+6x−8=−(6)2+6(6)−8=−36+36−8=−8

The minimum value is −8 .This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≥f(6) holds true.

Thus, the function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0) and the minimum value as −8 at the point (6,0) on the interval [1,6] .

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 4.9, Problem 1E

To determine

To calculate:The extrema of the function f(x)=−x2+6x−8 on the interval [1,6] .

Expert Solution & Answer

Answer to Problem 1E

The function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0)and the minimum value as −8at the point (6,0) on the interval [1,6] .

Explanation of Solution

Given information:

The function f(x)=−x2+6x−8 and the interval [1,6] .

Formula used:

If a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

Calculation:

Consider the function f(x)=−x2+6x−8 and the interval [1,6] .

Sketch the graph of the function f(x)=−x2+6x−8 on the coordinate axes.

Calculus : The Classic Edition (with Make the Grade and Infotrac), Chapter 4.9, Problem 1E

Observe that graph is a downward parabola.

Recall if a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

From the graph it is clear that function has maximum value at the point (3,0) . Evaluate the value of the function at the point.

f(3)=−x2+6x−8=−(3)2+6(3)−8=−9+18−8=1

The maximum value is 1. This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≤f(3) holds true.

From the graph it is clear that function has minimum value at the point (6,0) . Evaluate the value of the function at the point.

f(6)=−x2+6x−8=−(6)2+6(6)−8=−36+36−8=−8

The minimum value is −8 .This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≥f(6) holds true.

Thus, the function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0) and the minimum value as −8 at the point (6,0) on the interval [1,6] .

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 4.9, Problem 1E

To determine

To calculate:The extrema of the function f(x)=−x2+6x−8 on the interval [1,6] .

Expert Solution & Answer

Answer to Problem 1E

The function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0)and the minimum value as −8at the point (6,0) on the interval [1,6] .

Explanation of Solution

Given information:

The function f(x)=−x2+6x−8 and the interval [1,6] .

Formula used:

If a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

Calculation:

Consider the function f(x)=−x2+6x−8 and the interval [1,6] .

Sketch the graph of the function f(x)=−x2+6x−8 on the coordinate axes.

Calculus : The Classic Edition (with Make the Grade and Infotrac), Chapter 4.9, Problem 1E

Observe that graph is a downward parabola.

Recall if a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

From the graph it is clear that function has maximum value at the point (3,0) . Evaluate the value of the function at the point.

f(3)=−x2+6x−8=−(3)2+6(3)−8=−9+18−8=1

The maximum value is 1. This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≤f(3) holds true.

From the graph it is clear that function has minimum value at the point (6,0) . Evaluate the value of the function at the point.

f(6)=−x2+6x−8=−(6)2+6(6)−8=−36+36−8=−8

The minimum value is −8 .This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≥f(6) holds true.

Thus, the function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0) and the minimum value as −8 at the point (6,0) on the interval [1,6] .

Answer 6

Chapter 4.9, Problem 1E

To determine

To calculate:The extrema of the function f(x)=−x2+6x−8 on the interval [1,6] .

Expert Solution & Answer

Answer to Problem 1E

The function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0)and the minimum value as −8at the point (6,0) on the interval [1,6] .

Explanation of Solution

Given information:

The function f(x)=−x2+6x−8 and the interval [1,6] .

Formula used:

If a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

Calculation:

Consider the function f(x)=−x2+6x−8 and the interval [1,6] .

Sketch the graph of the function f(x)=−x2+6x−8 on the coordinate axes.

Calculus : The Classic Edition (with Make the Grade and Infotrac), Chapter 4.9, Problem 1E

Observe that graph is a downward parabola.

Recall if a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

From the graph it is clear that function has maximum value at the point (3,0) . Evaluate the value of the function at the point.

f(3)=−x2+6x−8=−(3)2+6(3)−8=−9+18−8=1

The maximum value is 1. This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≤f(3) holds true.

From the graph it is clear that function has minimum value at the point (6,0) . Evaluate the value of the function at the point.

f(6)=−x2+6x−8=−(6)2+6(6)−8=−36+36−8=−8

The minimum value is −8 .This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≥f(6) holds true.

Thus, the function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0) and the minimum value as −8 at the point (6,0) on the interval [1,6] .

Answer 7

Chapter 4.9, Problem 1E

To determine

To calculate:The extrema of the function f(x)=−x2+6x−8 on the interval [1,6] .

Answer 8

Expert Solution & Answer

Answer to Problem 1E

The function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0)and the minimum value as −8at the point (6,0) on the interval [1,6] .

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given information:

The function f(x)=−x2+6x−8 and the interval [1,6] .

Formula used:

If a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

Calculation:

Consider the function f(x)=−x2+6x−8 and the interval [1,6] .

Sketch the graph of the function f(x)=−x2+6x−8 on the coordinate axes.

Calculus : The Classic Edition (with Make the Grade and Infotrac), Chapter 4.9, Problem 1E

Observe that graph is a downward parabola.

Recall if a function g is defined on the set S which is a set of real numbers, and if a is any number in the set S , then g(a) is the maximum value of g on S if g(x)≤g(a) for each x in S and g(a) is the minimum value of g on S if g(x)≥g(a) for each x in S .

The maximum and minimum values are called extrema of the function g .

From the graph it is clear that function has maximum value at the point (3,0) . Evaluate the value of the function at the point.

f(3)=−x2+6x−8=−(3)2+6(3)−8=−9+18−8=1

The maximum value is 1. This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≤f(3) holds true.

From the graph it is clear that function has minimum value at the point (6,0) . Evaluate the value of the function at the point.

f(6)=−x2+6x−8=−(6)2+6(6)−8=−36+36−8=−8

The minimum value is −8 .This can be observed from graph also that for anyx lying between [1,6] , the condition f(x)≥f(6) holds true.

Thus, the function f(x)=−x2+6x−8 has maximum value as 1 at the point (3,0) and the minimum value as −8 at the point (6,0) on the interval [1,6] .

Answer 12

Ch. 4.9 - Prob. 1E Ch. 4.9 - Prob. 2E Ch. 4.9 - Prob. 3E Ch. 4.9 - Prob. 4E Ch. 4.9 - Prob. 5E Ch. 4.9 - Prob. 6E Ch. 4.9 - Prob. 7E Ch. 4.9 - Prob. 8E Ch. 4.9 - Prob. 9E Ch. 4.9 - Prob. 10E

The extrema of the function f ( x ) = − x 2 + 6 x − 8 on the interval [ 1 , 6 ] .

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To calculate:The extrema of the function f(x)=−x2+6x−8 on the interval [1,6] .

Answer to Problem 1E

Explanation of Solution

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Chapter 4.9 Solutions