Hello. I have a question related to curve sketching.

If g(x) is a twice differentiable function, which statement below is true(in regards to the following function)?

f(x)=g(x)+x^2

- if g'(x)<-2, on (0,1), then f(x) is increasing on (0,1)

-if g'(0) =0 ang g"(0)>0, then x=0 is a local maximum of f(x)

- if g'(x)>0 on (1,10), then f(10) the the absolute maximum on (1,10)

- if g'(x)<-3 on (0,2), the f(0) is the absolute minimum on (0,2)