Using the Graph, Determine Any Relative Maxima or Minima of the Function

question 151

Multiple Choice

Using the graph, determine any relative maxima or minima of the function and the intervals on which the function is
increasing or decreasing. Round to three decimal places when necessary.
- $f ( x ) = \frac { 1 } { 2 } x ^ { 3 } + \frac { 1 } { 2 } x ^ { 2 } - x + 1$

• A) relative maximum: 2.056 at x=-1.215 ; relative minima: 0.684 at x=0.549 and 1 at x=0 ; increasing (-1.215,0.549) ; decreasing \(( - \infty , - 1.215 ) , ( 0.549 , \infty )\)
• B) relative maximum: 0.684 at x=0.549 ; relative minimum: 2.056 at x=-1.215 ; increasing (-1.215,0.549) ; decreasing \(( - \infty , - 1.215 ) , ( 0.549 , \infty )\)
• C) no relative maxima or minima; increasing \(( \rightarrow \infty , - 1.215 ) , ( 0.549 , \infty )\) decreasing (-1.215,0.549)
• D) relative maximum: 2.056 at x=-1.215 ; relative minimum: 0.684 at x=0.549 ; increasing \(( \infty , - 1.215 ) , ( 0.549 , \infty )\) decreasing (-1.215,0.549)

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Having the personal drive or inner willingness to undertake activities without external encouragement.