Find the inflection point(s) of y = 2 $x ^ { 3 }$

Question

Find the inflection point(s) of y = 2 $x ^ { 3 }$ - 3 $x ^ { 2 }$ - 12x + 17.
A) $\left( \frac { 1 } { 2 } , \frac { 21 } { 2 } \right)$
B) $\left( \frac { 1 } { 2 } , \frac { 21 } { 2 } \right)$ and $- \frac { 1 } { 2 } , 22$
C) $\left( \frac { 7 } { 2 } , 24 \right.$ and $\left( \frac { 1 } { 2 } , \frac { 21 } { 2 } \right)$
D) (2, -3)
E) none of these

Quizplus · Accepted Answer

The inflection point is found by taking the second derivative and setting it equal to zero. The second derivative is 12x - 6. Setting this equal to zero gives x = 1/2. Plugging this back into the original equation gives y = 21/2. So the inflection point is (1/2, 21/2).

Find the Inflection Point(s) of Y = 2 x3x ^ { 3 }x3