Question

use the first derivative test to determine the local extrema values and any absolute extrema of the function:
y=3-x^2 if x<0
x^2 + 1 if x>=0

Answer 1

Find the derivative of each equation and set them equal to zero to find the critical points.

Answer 2

I strongly suggest that you try graphing this piecewise defined function. It appears to me that this function is discontinuous at x=0. Use the Draw utility (below).