# Piecewise Differentiable Equation?

1. Oct 14, 2011

### bman123

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. Oct 14, 2011

### spamiam

I think you're on the right track. Saying h is differentiable at x=2 actually gives you 2 conditions:

h is continuous, so $\lim_{x \to 2^-} h(x) = \lim_{x \to 2^+} h(x)$

h is differentiable, so $\lim_{x \to 2^-} h'(x) = \lim_{x \to 2^+} h'(x)$

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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