Determine all critical points for the function.
-$$f ( x ) = x ^ { 3 } - 12 x + 5$$
A) $x = - 2$ and $x = 2$
B) $x = 2$
C) $x = - 2$
D) $x = - 2 , x = 0$, and $x = 2$

Question

Quizplus · Accepted Answer

To find the critical points, we first find the derivative of the function $f(x) = x^3 - 12x + 5$, which is $f'(x) = 3x^2 - 12$. Setting the derivative equal to zero gives $3x^2 - 12 = 0$, or $x^2 = 4$. Solving for $x$ gives $x = -2$ and $x = 2$, which are the critical points.

Determine All Critical Points for the Function f(x)=x3−12x+5f ( x ) = x ^ { 3 } - 12 x + 5f(x)=x3−12x+5

Determine All Critical Points for the Function $f ( x ) = x ^ { 3 } - 12 x + 5$