Find the values of m and b that make the following function differentiable. f(x) = {x^2, x less than or equal to 2 mx+b, x> 2} you so

In order to be differentiable everywhere, must first be continuous everywhere, which means the limits from either side as must be the same and equal to . By definition, , and

so we need to have .

For to be differentiable at , the derivative needs to be continuous at , i.e.

We then need to have

Then