derivative help!?

Question

The first derivative of a function is given as y= the square root of (x + 2) for x <=2; and y= x -3 for x>=2. How do I find the original function and the second derivative?

Answer 1

To find the original function, integrate each of the two functions.

To find the second derivative, differentiate each of the two functions.

Then check that your answers make sense at x=2.

Now, it so happens that the first derivative isn't continuous at x=2, let alone differentiable. So caution at x=2 is indeed necessary.