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Describe how the graph of $f$ varies as $c$ varies. Graphseveral members of the family to illustrate the trends that youdiscover. 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.$$f(x)=e^{-c / x^{2}}$$

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Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 4

Curve Sketching

Derivatives

Differentiation

Applications of the Derivative

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Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

13:14

Describe how the graph of …

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01:47

07:24

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.

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