Which of the following functions grows the fastest as x goes to infinity? (2 points)
f(x) = ex
f(x) = 2x
f(x) = 4x
f(x) = e-2x
To determine which function grows fastest as x goes to infinity, we need to compare their growth rates.
1. f(x) = ex:
The exponential function, ex, grows at a rapid rate as x approaches infinity. The growth rate of an exponential function increases with every unit increase in x.
2. f(x) = 2x:
The function 2x is an exponential function as well, but with a base of 2 instead of e. While still growing, the growth rate of this function is slower compared to an exponential function with base e.
3. f(x) = 4x:
The function 4x is also an exponential function, but with a base of 4. Similar to the previous function, its growth rate is slower than that of ex.
4. f(x) = e-2x:
This function is an exponential function, but with a negative exponent. As x approaches infinity, the value of e-2x approaches 0, indicating that its growth rate diminishes significantly compared to the other functions.
Therefore, the function f(x) = ex grows the fastest as x goes to infinity among the given options.
Again, assuming you mean f(x) = e^x, and f(x) = e^(-2x)
using the same webpage as that I gave you in your previous post, change the equations and see what you get.
I hope you would be able to tell that an exponential function would grow the fastest.
Since you titled your posts "Calculus", why not take the derivative of each, and knowing what the first derivative represents should give you the answer.