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Use the methods of this section to sketch the curve $ y = x^3 - 3a^2 x + 2a^3 $, where $ a $ is a positive constant. What do the members of this family of curves have in common? How do they differ from each other?

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03:50

Wen Zheng

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Derivatives

Differentiation

Volume

Campbell University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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$$\begin{array}{l}{\te…

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Use the methods of this se…

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01:22

Graph the curves. Explain …

I say we sketched the graph like this. As you can see, if a is greater than zero, we can see the graph. And then for a equal zero, we conceded we would just have a cube function. Why equals X Cube? You know there's no local minimums or Maxima for a cubic function. Therefore, we know that when a is less than zero, the graphics shifted for a cube units down. So this is down.

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