Is that correct my resolution? (First derivative test-Increasing and decreasing functions)

Find the local and absolute maxima or minima for this function.

a) f(x)=x²+1

f'(x)=2x

2x=0
x=0

(-infinity,0)-> 2*(-1) decreasing
(0,+infinity)-> 2*(1) increasing

Conclusion: It has a local and a global minima of 1 at x=0

Yes- good job!

Yes