# 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

8 months ago

## To determine which function is increasing the fastest when x = 2, you can follow these steps:

1. Differentiate each function:
- For f(x) = x^2, the derivative f'(x) = 2x.
- For g(x) = e^(2x), the derivative g'(x) = 2e^(2x).
- For h(x) = ln(2x), the derivative h'(x) = 1/x.

2. Plug in x = 2 into the derivatives:
- f'(2) = 2(2) = 4
- g'(2) = 2e^(2*2) = 2e^4 ≈ 109.1
- h'(2) = 1/2 = 0.5

3. Compare the values obtained:
- Since g'(2) ≈ 109.1 is the largest value among f'(2) = 4 and h'(2) = 0.5, the function g(x) = e^(2x) is increasing the fastest at x = 2.

Therefore, g(x) = e^(2x) is the function increasing the fastest when x = 2.

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