# Thread: finding the first and second derivative of a peicewise function

1. ## finding the first and second derivative of a peicewise function

i need help finding the first and second derivative of this peicewise function

f(x)= { 2(x+1)^2 , x<1
{ -x^2 +9 , x >= 1

the two { are supposed to be one big {

oh and when you want to check for concavity and increasing and decreasing, do you check each function of the peicewise seperately?

2. $f'(x)=4(x+1),f''(x)=4 \text{ if }x<1;
f'(x)=-2x,f''(x)=-2 \text{ if }x>1$

the first and second derivative of f(x) at the point x=1 don't exist!

3. The important part to remember about integrating or differentiating piecewise functions is that you have to treat them in separate pieces, with the connecting values generally being discontinuous or non-differentiable.