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Tangent to both functions

  1. Oct 2, 2006 #1
    Here's a question from my Calc HW andI believe my approach is flawed...

    Two functions
    f(x) = x^2
    g(x) = -x^2 + 6x -5

    Find the two lines tangent to both functions

    I thought I could find the slope where f' and g' are equal so I did:

    f'(x) = 2x
    g'(x) = -2x + 6
    2x = -2x +6
    x = 1.5
    slope = 2(1.5) = 3

    BUT that slope doesn't work as this simply finds an x on the two graphs where the two graphs have the same slope.

    Help me please!

    THE given answers are
  2. jcsd
  3. Oct 2, 2006 #2


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    Homework Helper

    Assume the line of tangency is y = mx +c.

    Solve to find the point of intersection of y=mx + c with each of the two curves.

    Keep in mind that there is only one point of intersection (with each curve) and not two x-values.
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