Question

Which of the following functions grows the fastest as x goes to infinity?

Answer 1

https://gyazo.com/a75478538401ecf38324fc5fbe30837f
@jim_thompson5910 @freckles How would I know how fast they are growing?

Answer 2

look at the graph of their derivatives

Answer 3

Would I look at the growth of y as it progress down the x-axis?

Answer 4

f(x) = ln(x) ----> f ' (x) = 1/x

f(x) = log(2,x) ----> f ' (x) = 1/[x*ln(2)]

f(x) = x^2 ----> f ' (x) = 2x

f(x) = 2^x -----> f ' (x) = ln(2)*2^x

Answer 5

http://www.wolframalpha.com/input/?i=plot+ {y+%3D+2+x^2%2B7+x%2C+y+%3D+e^x%2C+y+%3D+e^x%2F4%2C+y+%3D+%28log%28x%29%29%2F%28log%284%29%29}+%2C+{x+%2C+-5+%2C+10}

Answer 6

ignore the numbers and signs...

Answer 7

Kinda hard to ignore them......

Answer 8

after you get those derivatives, plug in a large number (like x = 1000) into each derivative function and compare the outputs

Answer 9

2^x is the fastest, correct?

Answer 10

@jim_thompson5910

Answer 11

yep