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:

Competitive Market

A competitive market is a market structure characterized by a large number of buyers and sellers, where no single entity has the power to influence market prices significantly.

Free-rider Problem

A situation where individuals benefit from resources, goods, or services that they do not pay for, which can lead to underproduction or depletion of those resources.

Rivalry

The competitive relationship between firms in the market, striving to gain advantage over each other in terms of sales, market share, or innovation.

Nonexcludable

A characteristic of a good or service whereby it is not possible to prevent people who have not paid for it from having access to it.