(a) Explanation Given Information: The provided graph of the function f ( x ) = − 1 3 x 3 + x 2 + 8 x − 12 is Explanation: Consider the provided graph of the function f ( x ) = − 1 3 x 3 + x 2 + 8 x − 12 , Recall that if f ″ ( x ) > 0 and f ( x ) is concave up and if f ″ ( x ) < 0 and f ( x ) is concave down. From the graph, if x < 1 then graph is concave up and if x > 1 then the graph is concave down and at point x = 1 the graph changes its concavity (b) To determine Where f ′ ( x ) has relative maxima and relative minima for the provided graph of a function f ( x ) = − 1 3 x 3 + x 2 + 8 x − 12 . (c) To determine The values of f ′ ( x ) and f ″ ( x ) , the region where f ″ ( x ) > 0 , f ″ ( x ) < 0 and f ″ ( x ) = 0 and where f ' ( x ) has relative maxima and relative minima for the function f ( x ) = − 1 3 x 3 + x 2 + 8 x − 12 and graph each function f ′ ( x ) and f ″ ( x ) .

11th Edition

ISBN: 8220100546235

Author: Reynolds

Publisher: CENGAGE L

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Question

Chapter 10.2, Problem 23E

(a)

To determine

The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f(x)=−13x3+x2+8x−12.

(b)

To determine

Where f′(x) has relative maxima and relative minima for the provided graph of a function f(x)=−13x3+x2+8x−12.

(c)

To determine

The values of f′(x) and f″(x), the region where f″(x)>0, f″(x)<0 and f″(x)=0 and where f'(x) has relative maxima and relative minima for the function f(x)=−13x3+x2+8x−12 and graph each function f′(x) and f″(x).

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Chapter 10.2, Problem 22E

Chapter 10.2, Problem 24E

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Chapter 10 Solutions

EBK MATHEMATICAL APPLICATIONS FOR THE M

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...

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The region where f ″ ( x ) > 0 , f ″ ( x ) < 0 and f ″ ( x ) = 0 in the graph of the function f ( x ) = − 1 3 x 3 + x 2 + 8 x − 12 .

Solution Summary: The author explains the graph of the function f(x)=-13x

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The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f(x)=−13x3+x2+8x−12.

Where f′(x) has relative maxima and relative minima for the provided graph of a function f(x)=−13x3+x2+8x−12.

The values of f′(x) and f″(x), the region where f″(x)>0, f″(x)<0 and f″(x)=0 and where f'(x) has relative maxima and relative minima for the function f(x)=−13x3+x2+8x−12 and graph each function f′(x) and f″(x).

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Chapter 10 Solutions

The region where f ″ ( x ) &gt; 0 , f ″ ( x ) &lt; 0 and f ″ ( x ) = 0 in the graph of the function f ( x ) = − 1 3 x 3 + x 2 + 8 x − 12 .

Solution Summary: The author explains the graph of the function f(x)=-13x

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The region where f″(x)>0, f″(x)<0 and f″(x)=0 in the graph of the function f(x)=−13x3+x2+8x−12.

Where f′(x) has relative maxima and relative minima for the provided graph of a function f(x)=−13x3+x2+8x−12.

The values of f′(x) and f″(x), the region where f″(x)>0, f″(x)<0 and f″(x)=0 and where f'(x) has relative maxima and relative minima for the function f(x)=−13x3+x2+8x−12 and graph each function f′(x) and f″(x).

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Chapter 10 Solutions

The region where f ″ ( x ) > 0 , f ″ ( x ) < 0 and f ″ ( x ) = 0 in the graph of the function f ( x ) = − 1 3 x 3 + x 2 + 8 x − 12 .