burgerandcheese
Junior Member
- Joined
- Jul 2, 2018
- Messages
- 85
Hi. I need help with part (a) only because then I will be able to proceed to part (b)
I have no idea how to "deduce that xe-ax < M/x if x > c"
This is what I've done thus far:
f(x) = x2e-ax
f '(x) = xe-ax(2 - xa)
f ''(x) = e-ax(2 - 4ax + a2x2)
They are correct because I checked my answer using an online derivative calculator.
So setting f '(x) = 0 gives me x = 0 or x = 2/a
f ''(0) = 2 > 0 so f(x) is at its minimum when x = 0
f ''(2/a) = -2/e2 < 0 so f(x) is at its maximum when x = 2/a
So now c = 2/a > 0
M = f(2/a) = 4/(a2e2) > 0
How do I continue?