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How derivatives affect graphs homework help

  1. Nov 17, 2011 #1
    Hello All, This problem comes from #18 of section 4.3 out of stewarts 6th edition.

    The Question:

    Consider the following function:
    f(x)= e^(-x) * sqrt(x)

    What I am trying to find.

    a.) Find the intervals on which f is increasing and decreasing.
    b.) find any relative extrema.
    c.) find the intervals of concavity.
    d.) find all inflection points.

    For part a. I have taken the first derivative and got. 1/2x^-(1/2) *e^-x - e^-x * sqrt (x)

    after simplifying i got e^-x= 0
    and 1/2 x^-1/2 - sqrt x = 0

    I know i need to find these for my critical points but I am having difficulty proceeding.

    for extrema i know i plug in values between my critical points to see the critcal values.

    after that I know I take the 2nd derivative to find critical points for my concavity.

    thanks for your help!!
  2. jcsd
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