Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ The set of all critical numbers of ƒ is

A) $\left\{ - 1 , - \frac { 1 } { 3 } \right\}$
B) $\left\{ - 1 , \frac { 1 } { 3 } \right\}$
C) $\left\{ 1 , \frac { 1 } { 3 } \right\}$
D) $\left\{ 1 , - \frac { 1 } { 3 } \right\}$
E) $\{ 1 \}$

Question

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ The set of all critical numbers of ƒ is

A) $\left\{ - 1 , - \frac { 1 } { 3 } \right\}$
B) $\left\{ - 1 , \frac { 1 } { 3 } \right\}$
C) $\left\{ 1 , \frac { 1 } { 3 } \right\}$
D) $\left\{ 1 , - \frac { 1 } { 3 } \right\}$
E) $\{ 1 \}$

Quizplus · Accepted Answer

The critical numbers are found by setting the derivative $f'(x) = 3x^2 - 2x - 1$ to zero and solving for $x$. Solving $3x^2 - 2x - 1 = 0$ gives the roots $x = 1$ and $x = -\frac{1}{3}$.

Let f(x)=x3−x2−x+8f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8f(x)=x3−x2−x+8

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$