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Homework Help: Curve with stationary points

  1. Feb 12, 2010 #1
    1. The problem statement, all variables and given/known data
    A curve is defined for x<-2 by the equation y=((x^2)+3)sqr(x+2)

    a) Show that dy/dx=0 when x=-1 and find the x-coordinate of the other stationary point.

    b) Find the value of d^2y/dx^2 when x=-1 hence determine whether the turning point is max or min.


    2. Relevant equations



    3. The attempt at a solution
    y=((x^2)+3).(x+2)^1/2

    Differentiate by product rule : u=x^2 +3 v=(x+2)^1/2
    u'=2x v'=1/2((x+2)^1/2)

    dy/dx= (x^2+3).0.5(x+2)^(-0.5) + (x+2)^0.5 . 2x

    Where do i go from here>??
     
  2. jcsd
  3. Feb 12, 2010 #2
    Then sub in -1 and i get dy/dx=0.. but how do i find the second stat point?>?
     
  4. Feb 12, 2010 #3

    Mentallic

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    Homework Helper

    You need to solve dy/dx=0 like you would any other equation.
    Substituting in x=-1 doesn't help you since you already know it's a stationary point so of course you'll get an answer of dy/dx=0 for x=-1.
     
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