Use Descartes' Rule of Signs to Determine the Possible Number $f ( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } + 5 x + 1$

question 12

Multiple Choice

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of $f ( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } + 5 x + 1$ .

• A)3 positive reals or 1 positive real;3 negative reals or 1 negative real
• B)3 positive reals or 1 positive real;no negative reals
• C)0 positive real;3 negative reals or 1 negative real
• D)1 positive real;3 negative reals or 1 negative real
• E)no positive reals;no negative reals

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Definitions:

Total Cost

The overall expenditure incurred by a company in the production of goods or services, including fixed and variable costs.

Total Revenue

The total income generated from the sale of goods or services by a company.

Profitable One

An entity or venture that generates income exceeding its costs and expenses, thereby yielding a surplus or profit.

MC > MR

A condition where the marginal cost of producing an additional unit is greater than the marginal revenue gained from selling it, indicating it’s not profitable to increase production.