The Vertex of a Parabola Occurs Where the Derivative of Its

question 94

Multiple Choice

The vertex of a parabola occurs where the derivative of its equation is 0, so an equation associated with the equation of a
parabola can be solved to find the x-coordinate of the vertex. Find the vertex of the parabola, given the equation of the
parabola and its associated equation.
-Equation of parabola: $f ( x ) = x ^ { 2 } - 6 x + 1$ ; associated equation: $0 = 2 x - 6$

• A) \(( 3 , - 8 )\)
• B) \(( 3,28 )\)
• C) \(( - 3,28 )\)
• D) \(( - 3 , - 8 )\)

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Definitions:

Nash Equilibrium

Nash Equilibrium is a concept in game theory where each player's strategy is optimal given the strategies of all other players, leading to a situation where no player can benefit by changing strategies unilaterally.

Profit-Maximizing

A strategy or process by which a firm adjusts its production and pricing to achieve the highest profit possible.

Collude

To come to a secret understanding for a harmful purpose; often refers to competitors agreeing on prices or market shares to gain an advantage.

Annual Fixed Cost

Regular expenses incurred by a business or individual that do not vary with production level or output within a year.