Graph the equation. Include the coordinates of any local and absolute extreme points and inflection points.
-$y=x^{1 / 3}\left(x^{2}-63\right)$

A) no extrema inflection point: $( 0,0 )$
B) local minimum: $\left( \pm \sqrt { 27 } , - \frac { 27 } { 2 } \right)$ local maximum: $ (0,0) $ inflection points: $ (\pm 3,-5) $
C) local minimum: $ (3,-54 \sqrt[3]{3}) $ local maximum: $ (-3,54 \sqrt[3]{3}) $ inflection point: $ (0,0) $
D) local minimum: $ (0,0) $ no inflection points

Question

Graph the equation. Include the coordinates of any local and absolute extreme points and inflection points.
-$y=x^{1 / 3}\left(x^{2}-63\right)$

A) no extrema inflection point: $( 0,0 )$ 
B) local minimum: $\left( \pm \sqrt { 27 } , - \frac { 27 } { 2 } \right)$ local maximum: $ (0,0) $ inflection points: $ (\pm 3,-5) $ 
C) local minimum: $ (3,-54 \sqrt[3]{3}) $ local maximum: $ (-3,54 \sqrt[3]{3}) $ inflection point: $ (0,0) $ 
D) local minimum: $ (0,0) $ no inflection points

Quizplus · Accepted Answer

Option C has both local minimums and maximums as well as an inflection point, making it the best choice. Option A has only an inflection point, option B has only local extreme points and inflection points, and option D has only a local minimum.

Graph the Equation y=x1/3(x2−63)y=x^{1 / 3}\left(x^{2}-63\right)y=x1/3(x2−63) A) No Extrema Inflection Point (0,0)( 0,0 )(0,0)

Graph the Equation $y=x^{1 / 3}\left(x^{2}-63\right)$ A) No Extrema
Inflection Point $( 0,0 )$