#### burgerandcheese

##### Junior Member

- Joined
- Jul 2, 2018

- Messages
- 54

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) = x

^{2}e

^{-ax}

f '(x) = xe

^{-ax}(2 - xa)

f ''(x) = e

^{-ax}(2 - 4ax + a

^{2}x

^{2})

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/e

^{2}< 0 so f(x) is at its maximum when x = 2/a

So now c = 2/a > 0

M = f(2/a) = 4/(a

^{2}e

^{2}) > 0

How do I continue?