Determine the Zeros (If Any) of the Rational Function $g ( x ) = \frac { x ^ { 3 } - 64 } { x ^ { 2 } + 6 }$

question 42

Multiple Choice

Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 64 } { x ^ { 2 } + 6 }$ .

• A) \(x = - \sqrt { 6 } , x = \sqrt { 6 } , x = 4\)
• B)no zeros
• C) x = -4, x = 4
• D) x = 4
• E) \(x = - \sqrt { 6 } , x = \sqrt { 6 } , x = - 4 , x = 4\)

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Definitions:

Diseconomies of Scale

The condition in which a company or production process becomes less efficient as it grows larger, leading to increased costs per unit.

Long-Run Equilibrium

A state in which all factors of production and costs are variable, and firms make no economic profit or loss.

Long-Run Average Cost Curve

A graphical representation showing the minimum average cost of producing any given level of output when all inputs, including capital, are variable.

Short-Run Average Cost Curve

A graphical representation that shows how the average cost of production changes with varying output levels in the short term.