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A tangent line to both functions

  1. Jun 7, 2013 #1
    1. The problem statement, all variables and given/known data

    Determine a line that is tangent to both f(x)=x2 and g(x)=x2-2x

    2. Relevant equations

    3. The attempt at a solution
    f(x)=x2 => f'(x)=2x
    g(x)=x2-2x => g'(x)=2x-2

    f'(a) = f'(b)
    2a = 2b-2

    I don't know how to continue.
    Thanks for help.
     
  2. jcsd
  3. Jun 7, 2013 #2

    mfb

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    Staff: Mentor

    If h(x) is that line, what do you know about h(a), h(b)?
     
  4. Jun 7, 2013 #3
    Thank you.

    h(b) = (2b-2)b+c => c = -b2

    h(a) = (2b-2)a+c = (2b-2)a-b2 => (a-b)2+2a=0
    2a = 2b-1 => a = b-1
    (-1)2+2a=0 => a=-0.5 and b=0.5
     
  5. Jun 7, 2013 #4

    mfb

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    Staff: Mentor

    That is not true, but I think you mean 2(b-1).
    The result is right.
     
  6. Jun 7, 2013 #5
    Yes, I meant 2b-2.
     
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