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# hwsol5 - Math 140(07 Homework Set#5 Ae Ja Yee 4.1 Maximum...

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Math 140 (07), Homework Set #5 Ae Ja Yee 4.1 Maximum and Minimum Values 6. Use the graph to state the absolute and local maximum and minimum values of the function. Solution. There is no absolute maximum value; absolute minimum value is g (4) = 1; local maximum values are g (3) = 4 , g (6) = 3; local minimum values are g (2) = 2 and g (4) = 1. 32. Find the critical numbers of the function. f ( x ) = x 3 + x 2 + x Solution. f 0 ( x ) = 3 x 2 + 2 x + 1 = 0 x = - 2 ± 4 - 12 6 Neither of these is a real number. Thus there are no critical numbers. Find the absolute maximum and absolute minimum values of f on the given interval. 48. f ( x ) = x 3 - 6 x 2 + 9 x + 2, [ - 1 , 4] Solution. f 0 ( x ) = 3 x 2 - 12 x + 9 = 3( x - 1)( x - 3) = 0 x = 1 , 3 f ( - 1) = - 14 , f (1) = 6 , f (3) = 2 , f (4) = 6 So, f (1) + f (4) = 6 is the absolute maximum value and f ( - 1) = - 14 is the absolute minimum value. 52. f ( x ) = x 2 - 4 x 2 +4 , [ - 4 , 4]. Solution. f 0 ( x ) = ( x 2 + 4)(2 x ) - ( x 2 - 4)(2 x ) ( x 2 + 4) 2 = 16 x ( x 2 + 4) 2 = 0 x = 0 f ( ± 4) = 3 5 , f (0) = - 1 So, f ( ± 4) = 3 5 is the absolute maximum value and f (0) = - 1 is the absolute minimum value.

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hwsol5 - Math 140(07 Homework Set#5 Ae Ja Yee 4.1 Maximum...

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