Find the x-coordinate of the point of inflection of the function $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 1$ .
A) $- \frac { 3 } { 4 }$

B) $- \frac { 3 } { 2 }$

C) $\frac { 3 } { 4 }$

D) $- \frac { 1 } { 3 }$

E) $\frac { 3 } { 2 }$

F) $\frac { 1 } { 3 }$

G) $- \frac { 3 } { 4 }$.

H) $\frac { 2 } { 3 }$

Question

Find the x-coordinate of the point of inflection of the function $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 1$ .
A) $- \frac { 3 } { 4 }$

B) $- \frac { 3 } { 2 }$

C) $\frac { 3 } { 4 }$

D) $- \frac { 1 } { 3 }$

E) $\frac { 3 } { 2 }$

F) $\frac { 1 } { 3 }$

G) $- \frac { 3 } { 4 }$.

H) $\frac { 2 } { 3 }$

Quizplus · Accepted Answer

The point of inflection occurs where the second derivative changes sign. For $f(x) = x^3 - x^2 - x + 1$, the second derivative is $f''(x) = 6x - 2$. Setting $f''(x) = 0$ gives $6x - 2 = 0$, solving for $x$ gives $x = \frac{1}{3}$.

Find the X-Coordinate of the Point of Inflection of the Function