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

question 46

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

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