Question

Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = e−x − e−7x, [0, 1]

Answer 1

f = e^-x - e^-7x
f' = -e^-x + 7e^-7x
= e^-7x (7-e^6x)
f'=0 when e^6x = 7, or x = (ln7)/6

So, evaluate f at the end points and at that x, to get max and min for the interval.

To check, go to

http://rechneronline.de/function-graphs/

and enter

exp(-x) - exp(-7x)

for the function.
Set the x,y intervals to be 0 to 1