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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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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The spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.

Find the indefinite integral. Check Answer: 7x 4 + 1x dx

Chapter 4 Solutions

CALCULUS:EARLY TRANS.-SAPLINGPLUS

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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.