The region where the graph of f ( x ) is increasing and decreasing and the location relative extrema in the graph of the function f ′ ( x ) = 6 x 2 − x 3 .

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Answer 1

Question

Chapter 10, Problem 28RE

(a)

To determine

The region where the graph of f(x) is increasing and decreasing and the location relative extrema in the graph of the function f′(x)=6x2−x3.

(b)

To determine

To calculate: The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f′(x)=6x2−x3.

(c)

To determine

To prove: The derivative f′(x) is the derivative of f(x) and also check the conclusion from part (a) by draw the graph of f(x).

(d)

To determine

To calculate: The function f″(x) for the function f(x)=2x3−x44 and check the conclusion from part (b) by draw the graph of f″(x).

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Answer 2

Question

Chapter 10, Problem 28RE

(a)

To determine

The region where the graph of f(x) is increasing and decreasing and the location relative extrema in the graph of the function f′(x)=6x2−x3.

(b)

To determine

To calculate: The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f′(x)=6x2−x3.

(c)

To determine

To prove: The derivative f′(x) is the derivative of f(x) and also check the conclusion from part (a) by draw the graph of f(x).

(d)

To determine

To calculate: The function f″(x) for the function f(x)=2x3−x44 and check the conclusion from part (b) by draw the graph of f″(x).

Expert Solution & Answer

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Answer 3

Question

Chapter 10, Problem 28RE

(a)

To determine

The region where the graph of f(x) is increasing and decreasing and the location relative extrema in the graph of the function f′(x)=6x2−x3.

(b)

To determine

To calculate: The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f′(x)=6x2−x3.

(c)

To determine

To prove: The derivative f′(x) is the derivative of f(x) and also check the conclusion from part (a) by draw the graph of f(x).

(d)

To determine

To calculate: The function f″(x) for the function f(x)=2x3−x44 and check the conclusion from part (b) by draw the graph of f″(x).

Expert Solution & Answer

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Answer 4

Question

Chapter 10, Problem 28RE

(a)

To determine

The region where the graph of f(x) is increasing and decreasing and the location relative extrema in the graph of the function f′(x)=6x2−x3.

(b)

To determine

To calculate: The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f′(x)=6x2−x3.

(c)

To determine

To prove: The derivative f′(x) is the derivative of f(x) and also check the conclusion from part (a) by draw the graph of f(x).

(d)

To determine

To calculate: The function f″(x) for the function f(x)=2x3−x44 and check the conclusion from part (b) by draw the graph of f″(x).

Expert Solution & Answer

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Answer 5

Chapter 10, Problem 28RE

(a)

To determine

The region where the graph of f(x) is increasing and decreasing and the location relative extrema in the graph of the function f′(x)=6x2−x3.

(b)

To determine

To calculate: The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f′(x)=6x2−x3.

(c)

To determine

To prove: The derivative f′(x) is the derivative of f(x) and also check the conclusion from part (a) by draw the graph of f(x).

(d)

To determine

To calculate: The function f″(x) for the function f(x)=2x3−x44 and check the conclusion from part (b) by draw the graph of f″(x).

Answer 6

Chapter 10, Problem 28RE

(a)

To determine

The region where the graph of f(x) is increasing and decreasing and the location relative extrema in the graph of the function f′(x)=6x2−x3.

Answer 7

Chapter 10, Problem 28RE

(a)

To determine

The region where the graph of f(x) is increasing and decreasing and the location relative extrema in the graph of the function f′(x)=6x2−x3.

Answer 8

(b)

To determine

To calculate: The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f′(x)=6x2−x3.

Answer 9

(b)

To determine

To calculate: The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f′(x)=6x2−x3.

Answer 10

(c)

To determine

To prove: The derivative f′(x) is the derivative of f(x) and also check the conclusion from part (a) by draw the graph of f(x).

Answer 11

(c)

To determine

To prove: The derivative f′(x) is the derivative of f(x) and also check the conclusion from part (a) by draw the graph of f(x).

Answer 12

(d)

To determine

To calculate: The function f″(x) for the function f(x)=2x3−x44 and check the conclusion from part (b) by draw the graph of f″(x).

Answer 13

(d)

To determine

To calculate: The function f″(x) for the function f(x)=2x3−x44 and check the conclusion from part (b) by draw the graph of f″(x).

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 10.1 - 1. The x- values of critical points are found...Ch. 10.1 - Prob. 2CP Ch. 10.1 - Prob. 3CP Ch. 10.1 - Prob. 4CP Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - 3. Use the graph of in Problem 1 to identify at...Ch. 10.1 - 4. Use the graph of in Problem 2 to identify at...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...

The region where the graph of f ( x ) is increasing and decreasing and the location relative extrema in the graph of the function f ′ ( x ) = 6 x 2 − x 3 .

Solution Summary: The author explains that the graph of a function is increasing if x6 is positive and decreases when the first derivative is negative.

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The region where the graph of f(x) is increasing and decreasing and the location relative extrema in the graph of the function f′(x)=6x2−x3.

To calculate: The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f′(x)=6x2−x3.

To prove: The derivative f′(x) is the derivative of f(x) and also check the conclusion from part (a) by draw the graph of f(x).

To calculate: The function f″(x) for the function f(x)=2x3−x44 and check the conclusion from part (b) by draw the graph of f″(x).

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Chapter 10 Solutions