Help with Calc please!

Question

Which of the following functions grows the fastest as x grows without bound?

Options:

1)	f(x) = x2
2)	g(x) = x2 + 5x
3)	h =
4)	They all grow at the same rate.

Answer 1

f(x) = x², f''(x) = 2x

f(x) = x² + 5x f'(x) = 2x+5

f(x) = (x^4 + 2x)^1/2 f''(x) = (1/2)(4x^3 + 2)(x^4 + 2x)^-1/2

1 and 2 grow at the same positive rate of 2x from x=0 whereas 3 decays from x=0 to 1/2, then grows at a greater rate than 1. and 2.

Answer 2

2) grows fastest

take the derivative of each, the derivative is the growth rate

1) 2x

2) 2x + 5

3) 2x +2

2x+5>2x+2>2x

for 3), the 4th power of the square root of x is just x^2