Maxima and Minima: Find the x that makes (a/x)^x biggest.

Question

turingtest · Answer

Wolfram says it has no max, and I can't solve the equation after the derivative.

lollylau · Answer

:D

turingtest · Answer

LollyLau know that and is messing with me, right?

lollylau · Answer

no i dont use wolfram
didnt know
and didnt mean to mess with you :)

lollylau · Answer

anyone knows how to do min/max problems?
tip: where it is a local min/max, the derivative is 0.

lollylau · Answer

3 more mins

turingtest · Answer

The only time the derivative seems to be zero is at$$x=\frac{a}{e}$$but I can't solve it, I'm trusting wolf

lollylau · Answer

lol? youre correct!

turingtest · Answer

hooray!
but why does wolfram say it has no max?

lollylau · Answer

ask them
...

turingtest · Answer

oh I can solve it I guess...
because (a/x)^x is never zero
but I still don't get the critical point. Is it a max or...?

lollylau · Answer

its not (a/x)^x thats zero, its the SLOPE.

turingtest · Answer

for the derivative I have
(a/x)^x *(ln(a/x)-1)=0
and I only need to solve
(ln(a/x)-1)=0
which gives
x=a\e

is what I'm saying. Don't know what you mean about slope.