A Function Is Given $U ( x ) = 4 \left( x ^ { 3 } - x \right)$

question 80

Essay

A function is given.
(a) Find all the local maximum and minimum values of the function and the value of x at which each occurs.
(b) Find the intervals on which the function is increasing and on which the function is decreasing. State all answers correct to two decimal places.
$U ( x ) = 4 \left( x ^ { 3 } - x \right)$

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Definitions:

Cash Outflows

Money paid out by a business for its operational and investment activities.

Straight-Line Depreciation

A method of calculating the depreciation of an asset which assumes the asset will lose an equal amount of value each year over its useful life.

Payback Period

The amount of time it takes for an investment to generate an amount of income or cash equivalent to the cost of the investment.

Incremental After-Tax Income

The additional net income that results from implementing a new project or decision, after accounting for taxes.