Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 2 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 24 x - 72$
A) x = 2, 6
B) x = -4, -3, 0
C) x = 3, 4
D) x = 0, 3, 4
E) x = -4, -3

Question

Quizplus · Accepted Answer

To find the relative extreme points, we first find the derivative of the function and set it to zero to find critical points. The derivative is $f'(x) = 2x^2 - 14x + 24$. Setting $f'(x) = 0$ gives the equation $2x^2 - 14x + 24 = 0$. Solving this quadratic equation, we find the roots $x = 3$ and $x = 4$. These are the x-coordinates of the relative extreme points.

Find the X Coordinates of All Relative Extreme Points Of f