Explanation Procedure: For finding absolute extrema for function f ( x ) we have to put f ′ ( x ) = 0 and also see whether f ( x ) is increasing or decreasing Calculation: Given function is f ( x ) = − x 4 − 4 x 3 + 8 x 2 + 20 Now find f ' ( x ) f ' ( x ) = d d x ( − x 4 − 4 x 3 + 8 x 2 + 20 ) = − 4 x 3 − 12 x 2 + 16 x Putting f ' ( x ) = 0 − 4 x 3 − 12 x 2 + 16 x = 0 − 4 x ( x 2 + 3 x − 4 ) = 0 − 4 x ( x + 4 ) ( x − 1 ) = 0 Either x = 0 or x + 4 = 0 or x − 1 = 0 . x = 0 , x = − 4 , x = 1 All these points can be local maxima or local minimum or point of Inflexion according to the sign changes. Hence x = - 4 and x = 1 are point of local maximum as f ′ ( x ) changes sign from + v e to − v e

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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The value of absolute extrema for f ( x ) = − x 4 − 4 x 3 + 8 x 2 + 20 and also find points where they occurs.

Solution Summary: The author explains how to find absolute extrema for f(x) and find points where they occur.

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The value of absolute extrema for f(x)=−x4−4x3+8x2+20 and also find points where they occurs.

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Chapter 6 Solutions

The value of absolute extrema for f ( x ) = − x 4 − 4 x 3 + 8 x 2 + 20 and also find points where they occurs.

Solution Summary: The author explains how to find absolute extrema for f(x) and find points where they occur.

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To find: The value of absolute extrema for f(x)=−x4−4x3+8x2+20 and also find points where they occurs.

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Chapter 6 Solutions

To find:

The value of absolute extrema for f(x)=−x4−4x3+8x2+20 and also find points where they occurs.