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Investigate the family of curves $ f(x) = e^x - cx $. In particular, find the limits as $ x \to \pm \infty $ and determine the values of $ c $ for which $ f $ has an absolute minimum. What happens to the minimum points as $ c $ increases?

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03:14

Wen Zheng

01:24

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Derivatives

Differentiation

Volume

Campbell University

University of Nottingham

Boston College

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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Investigate the family of …

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(a) Investigate the family…

So we want to investigate the family of curves. Um And those curves are F of X equals E. To the X. In sc X. This is what we have here. And we're going to change the values for C. Like this. No. Um And we see That when C is equal to zero. Yes, it looks like the traditional cardiac function. When she is less than zero, we see that there isn't a minimum value um or when she is equal to zero, but when she is greater than zero, we see that there is a minimum value. As X goes to infinity, why goes to infinity. As X goes to negative infinity, why goes to infinity? So that would be the different ways of looking at it. And then when Y is negative as X goes negative infinity, why goes negative infinity? As X goes to positive infinity, Why goes to positive infinity? And then lastly when sequel, zero as X goes to infinity, why goes to zero And as X goes to positive infinity, why it goes to infinity.

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