Posted by **Jen** on Monday, December 11, 2006 at 4:05pm.

f(x) = x^2

g(x) = e^2x

h(x) = ln(2x)

which function is increasing the fastest when x = 2

How do I do this? TIA

I will assume that g(x) = e^2x = e^(2x) and now e^x * x . It is ambiguous the way you have written it

(1) Differentiate each function to get f'(x), g'(x) and h'(x)

(2) Plug in x = 2 to f', g'and h'

(3) See which is biggest

Example:

f'(x) = 2x f'(2) = 4

g'(x) = 2*e^2x g'(2) = 2*e^4 = 109.1

You finish it

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