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Piecewise Differentiable Equation?

  1. Oct 14, 2011 #1
    1. The problem statement, all variables and given/known data
    K and M are constants. If h is differentiable at x=2, what are the values of k and m.
    h(x)= kx^2 + 1, 0<x<2
    mx - 3, 2<x<5

    All of the "<" signs are "less than or equal to"

    2. Relevant equations Not sure



    3. The attempt at a solution I tried setting the two parts of the function equal to eachother and substituting 2 for x, but it doesn't work. Not sure what to do. ANy help would be greatly appreciated!
     
  2. jcsd
  3. Oct 14, 2011 #2
    I think you're on the right track. Saying h is differentiable at x=2 actually gives you 2 conditions:

    h is continuous, so [itex] \lim_{x \to 2^-} h(x) = \lim_{x \to 2^+} h(x)[/itex]

    h is differentiable, so [itex]\lim_{x \to 2^-} h'(x) = \lim_{x \to 2^+} h'(x)[/itex]

    Write out what each of these means using the definition of h, which should give you 2 equations with 2 unknowns.
     
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