Piecewise Differentiable Equation?

[bman123]

Homework Statement

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"

Homework Equations

Not sure

The Attempt at a Solution

I tried setting the two parts of the function equal to each other and substituting 2 for x, but it doesn't work. Not sure what to do. ANy help would be greatly appreciated!

 

[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.