Determine the maximum value of the function f(x) = 4e^(-x) - e^(x)
The Attempt at a Solution
1. I first found the derivative of the function and it turned out to be f`(x) = -4e^-x - e^x
2. I believe that to find the maximum value of this function, you need to find out values of x that would equal to 0. (Critical numbers)
Then after finding these crit numbers, you can judge by looking at them and see which value returns to be the highest.
My problem is i do not know how to factor this expression with euler's constant involved. Can anyone help? (I think you can factor e out, but then i dont get a smooth expression or any critical numbers.)
Edit: I just realized i wrote in the title to be number, but i meant expression.