Find the Value or Values Of $c$ That Satisfy the Equation $\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )$

Find the value or values of $c$ that satisfy the equation $\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )$ in the conclusion of the Mean Value Theorem for the function and interval.
-An approximation to the total profit (in thousands of dollars) from the sale of $x$ hundred thousand tires is given by $p = - x ^ { 3 } + 15 x ^ { 2 } - 48 x + 450 , x \geq 3$ . Find the number of hundred thousands of tires that must be sold to maximize profit.

A) 5 hundred thousand
B) 3 hundred thousand
C) 10 hundred thousand
D) 8 hundred thousand