Problem

Describe how the graph of $f$ varies as $c$ varie…

Problem 63 Easy Difficulty

Describe how the graph of $f$ varies as $c$ varies. Graph
several members of the family to illustrate the trends that you
discover. In particular, you should investigate how maximum and minimum points and inflection points move when $c$ changes. You should also identify any transitional values of $c$ at which the basic shape of the curve changes.
$$f(x)=e^{-c / x^{2}}$$

Name: describe how the graph of f varies as c varies graph several members of the family to illustrate 19
Uploaded: 2020-09-22
Duration: 57 s
Channel: Numerade
Description: Describe how the graph of $f$ varies as $c$ varies. Graph several members of the family to illustrate the trends that you discover. In particular, you should investigate how maximum and minimum points and inflection points move when $c$ changes. You should also identify any transitional values of $c$ at which the basic shape of the curve changes. $$f(x)=e^{-c / x^{2}}$$

Answer

the transitional value is $0 .$ When $c$ is positive, the graphs come close to the $x$ -axis as $c$ increases. When $c$ is negative, there is a vertical asymptote at $x=0$ and the
graphs go further away from $y$ - axis as $c$ increases.

Topics

Derivatives

Differentiation

Applications of the Derivative

Essential Calculus Early Transcendentals

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 4

Curve Sketching

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Video Transcript

So I've graphed two versions of dysfunction with different See values here at negative one and a positive one. And you can see that Well, basically, as this graph kind of approaches zero, this is a transitional point at which e to the zero would be one. And so it would just be a flat line at y equals one. But once it starts to decrease its values, then the conch avid he flips. So it goes from these con cave down sections to these con cave up sections, and that happens on the other side as well. And so the graph as you decrease kind of flips this way, or as you increase goes the opposite way here, and no matter what value of how big it gets, it never goes below the ax access here as well.

Stephen H.

University of Utah