Explanation Given: The function f ( x ) is, f ( x ) = ( 2 x − x 2 ) e x ..... (1) Concept used: If f ″ ( c ) = 0 or f ″ ( c ) does not exist and the second derivative at changes sign at x = c , then f has a point of inflection at x = c . Graph: To graph the function, first make a table of set of values of x and f ( x ) . Then plot the points from the table and join the points to obtain the graph. Substitute − 3 for x in equation (1) to obtain the corresponding value of f ( x ) as, f ( − 3 ) = ( 2 ( − 3 ) − ( − 3 ) 2 ) ⋅ e − 3 = ( − 6 − 9 ) ⋅ 0.05 = − 0.75 Substitute − 2 for x in equation (1) to obtain the corresponding value of f ( x ) as, f ( − 2 ) = ( 2 ( − 2 ) − ( − 2 ) 2 ) ⋅ e − 2 = ( − 4 − 4 ) ⋅ 0.135 = − 1.08 Substitute 0 for x in equation (1) to obtain the corresponding value of f ( x ) as, f ( 0 ) = ( 2 ( 0 ) − ( 0 ) 2 ) ⋅ e 0 = ( 0 − 0 ) ⋅ 0.05 = 0 Substitute 1 for x in equation (1) to obtain the corresponding value of f ( x ) as, f ( 1 ) = ( 2 ( 1 ) − ( 1 ) 2 ) ⋅ e 1 = ( 2 − 1 ) ⋅ 2.72 = 2.72 Substitute 2 for x in equation (1) to obtain the corresponding value of f ( x ) as, f ( 2 ) = ( 2 ( 2 ) − ( 2 ) 2 ) ⋅ e 2 = ( 4 − 4 ) ⋅ 7.4 = 0 Now, make the table with the set of values as shown in Table 1. x f ( x ) − 3 − 0.75 − 2 − 1.08 0 0 1 2.72 2 0 Table 1 Now, plot the points and join them to obtain the graph of the function f ( x ) . The graph of the function f ( x ) is shown in Figure 1. Interpretation: From Figure 1, it is observed that the concavity changes from up to down around x = − 2 and the concavity changes from down to up at x = 1

4th Edition

ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.4, Problem 3E

To determine

To graph:

The function f(x)=(2x−x2)ex and find the points of inflection.

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Chapter 4.4, Problem 2E

Chapter 4.4, Problem 4E

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Chapter 4 Solutions

CALCULUS:EARLY TRANS.-SAPLINGPLUS

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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To graph: The function f ( x ) = ( 2 x − x 2 ) e x and find the points of inflection.

Solution Summary: The author explains how to graph the function f(x) and find the points of inflection.

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To graph:

The function f(x)=(2x−x2)ex and find the points of inflection.

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Chapter 4 Solutions

To graph: The function f ( x ) = ( 2 x − x 2 ) e x and find the points of inflection.

Solution Summary: The author explains how to graph the function f(x) and find the points of inflection.

Videos

To graph: The function f(x)=(2x−x2)ex and find the points of inflection.

Want to see the full answer?

Chapter 4 Solutions

To graph:

The function f(x)=(2x−x2)ex and find the points of inflection.