Use a Graphing Utility to (A) Plot the Graphs of the Given

question 38

Essay

Use a graphing utility to (a) plot the graphs of the given functions and (b) find the approximate $x$ -coordinates of the points of intersection of the graphs. Then find an approximation of the volume of the solid obtained by revolving the region bounded by the graphs of the functions about the $x$ -axis. Round answers to two decimal places.
$$y = \frac { 1 } { 5 } x ^ { 5 } , \mathrm { y } = 3 x ^ { 2 } - x ^ { 3 }$$

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Definitions:

Neural Activity

The operation of nerve cells (neurons) which involves the generation and transmission of electrical and chemical signals.

Caffeine

A stimulant found in coffee, tea, and various other beverages that affects the central nervous system, resulting in increased alertness and reduced fatigue.

Withdrawal

The process or experience of stopping or reducing the use of a psychoactive substance, characterized by physical and mental symptoms that vary based on the substance.

Drug Tolerance

The body's reduced response to a drug with repeated use, requiring higher doses to achieve the same effect.