Use a Graphing Utility to Graph the Function Over the Indicated

question 260

Multiple Choice

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two
decimal places.
- $$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 1 ; ( - 5,5 )$$

• A) local minimum at \(( 2 , - 3 )\)
• B) local maximum at \(( 0,1 )\)
• local minimum at \(( 2 , - 3 )\)
• C) local minimum at \(( 0,1 )\)
• local maximum at \(( 2 , - 3 )\)
• D) none

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Definitions:

Diminishing Returns

The principle stating that as one factor of production is increased while others are held constant, a point will eventually be reached where additions of the factor yield progressively smaller increases in output.

Value Added

The increase in worth of a product or service as a result of a particular stage of production or as it moves through the supply chain.

Marginal Product

The increase in output resulting from a one-unit increase in the amount of a single input used, keeping all other inputs constant.

Premium

A premium is the amount paid for an insurance policy, representing the price for the insurance coverage or the amount over the nominal value of something.