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Sketch the graph of a function that satisfies all of the given conditions.$f^{\prime}(x)>0$ if $|x|<2, \quad f^{\prime}(x)<0$ if $|x|>2$$f^{\prime}(-2)=0, \quad \lim _{x \rightarrow 2}\left|f^{\prime}(x)\right|=\infty, \quad f^{\prime \prime}(x)>0$ if $x \neq 2$

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Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

Derivatives

Differentiation

Applications of the Derivative

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Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

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this is one off the example I for this question. So we can see for this graph the function is always oh, can cave. I poured, except for this singular point X equals that you're back. Um, except for this single points that the graphics can keep up and the function is increasing from minus 2 to 2, and these decreasing otherwise. And it has, um, local minimum at X equals minus two. And he also has a vertical A symptomatic, um, at X equals two.

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