Question

Determine the maximum value of the function f(x)=4e^(-x) - e^x on the interval -1<=x<=2.

I first found the derivative: f'(x)=-4e^(-x) - e^x
Then I set it two zero. My problem is that I don't know how to isolate x

Answer 1

-4e^-x -e^x = 0 e^x = -4 e^-x
e^x/e^-x = -4
e^2x = -4

Answer 2

-4e^(-x) - e^(x) = 0
e^(x) = -4e^(-x)
e^(2x) = -4
2x = ln(-4)
x = 0.5*ln(-4), not real number.
That means that there is no maximum or minimum.
BUT, we have an interval [-1, 2], so we just need to check the maximum in the boundaries.

f(-1) = 10.505...
f(2) = -6.8477...
So, the maximum for the given interval is when x = -1

Answer 3

Oh, i got it now thanks!

Answer 4

No problem ;)

Answer 5

I have a question. Was -1 and 2 subbed into the derivative?

Answer 6

No, the derivative is used to find if there is a point in which the graph as slope 0 and that doesn't happen with this function

Answer 7

Oh ok i fixed my mistake!

Answer 8

so, we have to test the boundaries of f(x) and check the local max or min in a interval

Answer 9

Ok thanks again!