   Chapter 4, Problem 39RE

Chapter
Section
Textbook Problem

Graph f ( x ) = e − 1 / x 2 in a viewing rectangle that shows all the main aspects of this function. Estimate the inflection points. Then use calculus to find them exactly.

To determine

To sketch: The graph of the given function f(x)=e1x2 so that all the important aspects of the graph are visible and to estimate the inflection points and verify them with help of calculus.

Explanation

Use online graphing calculator to plot the graph of the function f(x)=e1x2 as shown in below Figure 1.

Zoom in the above graph so that the nature of the graph is more visible as shown in below Figure 2.

In the above graph observe that there is no local minimum or maximum for the given function also graph shows that there is no asymptote to the graph.

Function is symmetric about the y-axis and even.

Differentiate the given function with respect to x twice.

f(x)=e1x2f(x)=e1x2(2x3)f(x)=4e1x26x2e1x2x6

Plot the graph of f(x) by using online graphing calculator as shown in below Figure 3.

From the graph in Figure 3 observe that graph is concave downward on (0

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