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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Definitions:

Frequent Constipation

A condition characterized by infrequent bowel movements or difficulty passing stool that occurs on a regular basis.

Osteoporosis

A bone disease characterized by decreased bone mass and density, leading to increased risk of fractures, often occurring with age.

Bone Density

A measure of the amount of minerals (such as calcium) contained in a certain volume of bone, indicating its strength and risk of fracture.

Brittleness

describes a material's tendency to fracture or break without significant deformation or distortion.