Thread: 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?

thanks in advance

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

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.