Solve the Problem $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 11 x - 4$

question 10

Essay

Solve the problem.
-For the polynomial funct $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 11 x - 4$
a) Find the x- and y-intercepts of the graph of f. Round to two decimal places, if necessary.
b) Determine whether the graph crosses or touches the x-axis at each x-intercept.
c) End behavior: find the power function that the graph of f resembles for large values of |x|.
d) Use a graphing utility to graph the function.Approximate the local maxima rounded to two decimal places,
if necessary. Approximate the local minima rounded to two decimal places, if necessary.
e) Determine the number of turning points on the graph.
f) Put all the information together, and connect the points with a smooth, continuous curve to obtain the
graph of f.

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Definitions:

Interest

The expense associated with taking out a loan, usually represented as a yearly percent of the total loan value.

Years

A measurement of time equal to 365 days (or 366 days in a leap year), used to denote the duration or age of something.

Insurance Annuity

An insurance product that pays out income, typically used as a retirement strategy to provide individuals with a steady income in their post-work years.

Rate of Return

Net profit or net loss from an investment during a specified time span, presented as a percentage of the investment's initial financial input.