Answer the Problem $f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4 x + 3 , [ - 0.5,1.8 ]$

question 278

Essay

Answer the problem.
-Use the following function and a graphing calculator to answer the questions.
$f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4 x + 3 , [ - 0.5,1.8 ]$
a). Plot the function over the interval to see its general behavior there. Sketch the graph below.

b). Find the interior points where f = 0 (you may need to use the numerical equation solver to approximate a solution). You may wish to plot f as well. List the points as ordered pairs (x, y).
c). Find the interior points where f does not exist. List the points as ordered pairs (x, y).
d). Evaluate the function at the endpoints and list these points as ordered pairs (x, y).
e). Find the function's absolute extreme values on the interval and identify where they occur.

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Definitions:

Stockholders' Equity

The residual interest in the assets of a corporation that remains after deducting liabilities, representing ownership interest held by shareholders.

Current Ratio

A liquidity ratio that measures a company's ability to pay short-term obligations or those due within one year, calculated as current assets divided by current liabilities.

Net Plant

The total value of a company's property, plant, and equipment minus accumulated depreciation, representing the net book value of physical assets used in operations.

Operating Cycle

This refers to the period of time it takes for a business to purchase inventory, sell products, and receive cash from sales.