Find the Exact Location of All the Relative and Absolute $( - \infty , \infty )$

question 38

Multiple Choice

Find the exact location of all the relative and absolute extrema of the function with domain $( - \infty , \infty )$ . $g ( x ) = \frac { 1 } { 4 } x ^ { 4 } - \frac { 2 } { 3 } x ^ { 3 } + \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 2 }$

• A) \(\left( 0 , \frac { 1 } { 5 } \right)\) - absolute maximum
• B) \(\left( 0 , \frac { 1 } { 5 } \right)\) - absolute minimum
• C) \(\left( 0 , \frac { 1 } { 3 } \right)\) - relative maximum
• D) \(\left( 0 , \frac { 1 } { 2 } \right)\) - absolute minimum
• E) \(( 0,1 )\) - relative maximum

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