Question

If a piecewise function is broken up, then does it have a derivative?

Answer 1

What does broken up mean?

Answer 2

Example:

Answer 3

if "broken up" means discontinous then no, it will not have a derivative at the point of discontinuity

Answer 4

It can still have localized derivatives. As a whole however, it doesn't have a derivative.

Answer 5

it is necessary for a function to be continuous at a point (number) if it is going to have a derivative at that number

Answer 6

what kinggeorge said. the derivative will exist most places, just not at the point of discontinuity

Answer 7

If we're looking at this graph as one function, then no derivative?

Answer 8

Suppose your function is\[f(x)=\begin{matrix} x^2 & \quad x>0 \\ x+1 & \quad x \leq 0 \end{matrix}\] Then it has a derivative over the interval \((-\infty, 0)\) and \((0, \infty)\) but if you're looking at it as one function, it has no derivative.