The Vertex of a Parabola Occurs Where the Derivative of Its

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 $x = - 8$ and $x = - 1$ , the largest value of the expression $y = x ^ { 3 } + 12 x ^ { 2 } + 36 x + 9$ occurs where $3 x ^ { 2 } + 24 x + 36 = 0$ . Of the values of $x$ that satisfy $3 x ^ { 2 } + 24 x + 36 = 0$ , which gives the maximum value of $y = x ^ { 3 } + 12 x ^ { 2 } + 36 x + 9 ?$

A) $x = - 1$
B) $x = - 7$
C) $x = - 2$
D) $x = - 6$