Let $f ( x ) = x \left| x ^ { 3 } \right|$

question 126

Short Answer

Let $f ( x ) = x \left| x ^ { 3 } \right|$ .
a. Sketch the graph of $f$ .
b. For what values of $x$ is $f$ differentiable?
c. Find a formula for $f ^ { \prime } ( x )$ .

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Definitions:

Uniformly Distributed

Uniformly distributed indicates that all outcomes in a data set or probability distribution have the same or nearly equal chance of occurring.

Standard Deviation

A tool to determine the degree of difference or dispersion within a batch of data.

Standard Normal

A type of normal distribution with a mean of 0 and a standard deviation of 1.

Random Variable

A numerical value variable resulting from random phenomena.