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Math Help - Natural Logs

  1. #1
    Feb 2009

    Natural Logs

    Hi I have a pair of questions that are becoming slowly irritating any help would be greatly appreciated.

    Determine where y=(x+1)^4 (e^-x) is increasing and decreasing


    Determine the critical numbers and points of inflection for y= x^2 (e^-2x)
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  2. #2
    MHF Contributor Calculus26's Avatar
    Mar 2009
    For the first one
    dy/dx = 4(x+1)^3 e^(-x ) -(x+1)^4e^(-x)

    = e^(-x)*(x+1)^3[ 3-x]

    the zeroes are x =-1 and 3

    Use either a graph or test pts to determine sign on intervals (-inf,-1)
    (-1,3) and (3,inf)

    Remember any exponential is always positve so you can simplify

    by considering (x+1)^3[ 3-x] only

    In part 2 it works the same except you also have to consider the second derivative as well
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