Question

Show that f(x) = x^2 and g(x) = 1000x^2 grow at the same rate.

Answer 1

You do not use the first derivative to find the rate you need to take the limit ratio as x approaches positive infinity. We use positive and not negative infinity because our function is increasing and not decreasing. The ratio ends up being 1/1000 meaning that this a finite non zero number. Which proves that they grow at the same rate

Explanation:

Answer 2

The rate of growth is the first derivative.

f(x) = x2

f'(x) = 2x

g(x) = 1000x2

g'(x) = 2000x

f'(x) ≠ g'(x)

f(x) and g(x) DO NOT grow at the same rate.