Sketch the Graph and Show All Local Extrema and Inflection $= - x ^ { 4 } + 2 x ^ { 2 } - 10$

Multiple Choice

Sketch the graph and show all local extrema and inflection points.
-y $= - x ^ { 4 } + 2 x ^ { 2 } - 10$

A) Absolute maxima: $( - 1 , - 9 ) , ( 1 , - 9 )$
Inflection points: $\left( - \sqrt { \frac { 1 } { 3 } } , 1 \right) , \left( \sqrt { \frac { 1 } { 3 } } , 1 \right)$


B) Absolute maxima: $( - 1 , - 9 ) , ( 1 , - 9 )$
Local minimum: $( 0 , - 10 )$ No inflection points


C) Absolute minima: $( - 1,9 ) , ( 1,9 )$
Inflection point: $\left( - \sqrt { \frac { 1 } { 3 } } , \frac { 85 } { 9 } \right) , \left( \sqrt { \frac { 1 } { 3 } } , \frac { 85 } { 9 } \right)$


D) Absolute maxima: $( - 1 , - 9 ) , ( 1 , - 9 )$ Local maximum: $( 0,10 )$ Local minimum: $( 0 , - 10 )$

Inflection points: $\left( - \sqrt { \frac { 1 } { 3 } } , 1 \right) , \left( \sqrt { \frac { 1 } { 3 } } , 1 \right)$