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SOLUTIONS EXERCISE 12 1) a) y =x3 ? y / = 3x 2 ? y // = 6x CHAPTER 12 high up / Below x-axis: y =0 ? x3 =0 ? x =0 y=x 3 0 + y faint: nowhere Thus y is to a lower wander the x-axis when x ? ( ??;0 ) and y is above x-axis when x ? ( 0; ? ) . Increase / diminish: y/ =0 ? 3x 2 = 0 ? x =0 y = 3x / 2 0 + + y / indefinite: nowhere Hence y increases when x ? ( ??;0 ) ? ( 0; ? ) and y has NO sex scrap extremes. incurvation: y // = 0 y // ? 6x = 0 ? x =0 y = 6x // undefined: nowhere 0 + y is saucer-shaped downwardly when x ? ( ??;0 ) and is saclike upwards when x ? ( 0; ? ) . Inflection signifys: x =0 ? y = (0)3 = 0 frankincense ( 0;0 ) is an inflection doom of y 9 y y= x³ analysis: 0 y y/ y // ? + ? + + + -3 x 3 -9 _ 1 1 b) y = 3 x 3 + 2x + 9 ? y / = 9x 2 + 2 ? y // = 18x Increase / shine: y/ = 0 ? 9x2 + 2 = 0 ? 9 x 2 = ?2 never (?x ? », x 2 ? 0 ) y / undefined: nowhere Hence ?x ? » , y?( x ) > 0 , therefore y increases on ( ? ? ; ? ) . there are no sexual intercourse extremes.

incurvation: y // = 0 y // ? 18x = 0 ? x =0 y = 18x // 0 + undefined: nowhere y is pouchlike downwards when x ? ( ? ? ; 0 ) and is concave upwards when x ? ( 0 ; ? ) Inflection points: x =0 ? y = 3(0)3 + 2(0) + 9 = 9 thus ( 0 ; 9 ) is the inflection point. Summary: 0 y/ y // + ? + + 18 y (0; 9) y = 3x3 + 2 x + 9 x 3 3 2 1 c) y = ?x 5 ? 5x 4 + 200 ? y / = ?5x 4 ? 20x 3 ? y // = ?20x 3 ? 60x 2 Increase / ebb: y/ =0 / ? ? 5x 4 ? 20x 3 = 0 x =0 ? ? ? 5x 3 ( x + 4) = 0 4 y = 5x (x+4) / 3 x = ?4 0 + y undefined: nowhere Hence, y decreases when x ? ( ??; ?4 ) ? ( 0; ? ) and y increases when x ? ( ?4;0 ) Relative minimum hold dear at Relative supreme at x = ?4 of y = ?( ?4)5 ? 5( ?4)4 + 200 = ?56 ? ( ?4 ; ?56) x = 0 of y = ?(0)5 ? 5(0)4 + 200 = 200 ? (0 ; 200) concaveness: y // = 0 ? ? ?...If you want to add a full essay, crop it on our website: Ordercustompaper.com

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