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Homework Help: Using IVT and RT

  1. Dec 27, 2009 #1
    "Using IVT and RT work out an estimate for the smallest distance between the point (0,0) and the curve
    y = e^x "
    Can anyone help me with this question? Thanks.


    Note: IVT is "Intermediate Value Theorem" and RT is "Rolle's Theorem"
     
  2. jcsd
  3. Dec 28, 2009 #2
    What is the function for distance between the points (0,0) and (x,e^x)?
     
  4. Dec 29, 2009 #3

    mathman

    User Avatar
    Science Advisor

    d2=x2+e2x

    RT says there is a point where the tangent (to d2) is horizontal, since the function ->+∞ for both x and -x ->∞. This would be the minimum.

    Use IVT on the derivative of x2 lets you find the minimum (0 derivative), since the derivative goes to +∞ as x goes to +∞, while it goes to -∞ as x goes to -∞.
     
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