Compare the growth rate of the functions f(x) = x^3 + 1 and g(x) = x^2

Question

Compare the growth rate of the functions f(x) = x³ + 1 and g(x) = x²

^A)f(x) grows faster than g(x).

^B)g(x) grows faster than f(x).

^C)f(x) and g(x) grow at the same rate.

^D)It cannot be determined.

My answer is A

Answer 1

A) is correct

in general.

but for the interval 0<x<1, f(x) grows from 1 to 2, g(x) grows from 0 to 1

1 to 2 is a 100% increase. 0 to 1 is an infinite % increase