The Vertex of a Parabola Occurs Where the Derivative of Its

question 261

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.
-Between $x = - 2$ and $x = 10$ , the largest value of the expression $y = x ^ { 3 } - 12 x ^ { 2 } - 9$ occurs where $3 x ^ { 2 } - 24 x = 0$ . Of the values of $x$ that satisfy $3 x ^ { 2 } - 24 x = 0$ , which gives the maximum value of $y = x ^ { 3 } - 12 x ^ { 2 } - 9$ ?

• A) \(x = 8\)
• B) \(x = 2\)
• C) \(x = 7\)
• D) \(x = 0\)

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