Mathamatics

1 ) commence the absolute maximum and minimum values aside (x x3-3x 1 on the interval x is either less(prenominal) than or make up to 3 or greater than or constitute to 0SolutionGet the derivativef (x 3 x2-3Equate to 0 and solve for x0 3 x2-3x2 3 /3The square root of 1 is 1 and -1 , therefore the ii values arex1 1x2 -1This is confirmed by the graph shown belowSolve for the intervals that is less than or equal to 3 or greater than or equal to 0Maximumfmax f (-1 (-1 )3-3 (-1 1 3Minimumfmin f (1 (1 )3-3 (1 1 -12 ) find the local maximum and minimum values off (x x5 - 5x 3 usinga ) The base derivative running playSolutionGet the derivativef (x 5x4 - 5Equate to 0 and solve for x0 5x4 - 5x4 (5 /5x 1 or -11st derived screen for x 1f (0 .9 -1 .72f (1 .1 2 .32Since f (0 .9 ) is prejudicious and f (1 .1 ) is positive and then it i s a local minimum1st Derivative test for x -1f (-1 .1 2 .32f (-0 .9 -1 .72Since f (-1 .1 ) is positive and f (-0 .

9 ) is negative then it is a local maximumb ) The arc second derivative testSolutionGet the second derivativef (x 20x2nd Derivative test for x 1f (1 20Since f (x 0 then it is local minimum2nd Derivative test for x 1f (-1 -20Since f (x 0 then it is local maximumc ) Which do you opt ? WhyI like the second derivative test since it is easier to evaluate and compare3 ) hazard the closely cosmopolitan antiderivative (add a constant ) of f (x 3x2 1 / x (where x is greater than 0SolutionAx (f (x F (x (3 /3 )x3 lnx CF (x x3 lnx C4 (a ) Find the most g! eneral antiderivative F of f (x 1 - sin xSolutionF (x x - (-cosx CF (x x cosx C (b ) Find the Antiderivative which satisfiesF (0 0Solution0 0 cos (0 CC - cos (0C -1Therefore the equation isF (x x cosx - 1...If you want to add up a full essay, edict it on our website: OrderCustomPaper.com

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