Find all the critical numbers of the function $f ( x ) = x ^ { 3 } - 3 x - 2$ .
A) None
B) -1, 1
C) 0, -1, 1
D) $- \sqrt [ 3 ] { 2 }$

Question

Quizplus · Accepted Answer

Critical numbers of a function occur where its derivative is zero or undefined. The derivative of $f(x) = x^3 - 3x - 2$ is $f'(x) = 3x^2 - 3$. Setting this equal to zero gives $3x^2 - 3 = 0$, or $x^2 = 1$, which has solutions $x = -1$ and $x = 1$. These are the critical numbers of the function.

Find All the Critical Numbers of the Function f(x)=x3−3x−2f ( x ) = x ^ { 3 } - 3 x - 2f(x)=x3−3x−2

Find All the Critical Numbers of the Function $f ( x ) = x ^ { 3 } - 3 x - 2$