Question

Which function increases at a faster rate on 0 to infinity,f(x)=x2 or g(x)=2x

Answer 1

For the domain x<=0:

f(x) = x^2 will increase at a faster rate because the rate of change of gradient is increasing, by contrast for the function:
g(x) = 2x, the rate of change of gradient is 0 (always remains at 2).

Therefore f(x) = x^2 increases at a faster rate.