A rectangle has one side on the positive x-axis, one side on the positive y-axis, and its upper right-hand vertex on the curve y = e^-4x. What dimensions (LxH) give the rectangle its largest area and what is that area? :)

1/4 x 1/e with an area of 1/4e. Looks more like a calculus 1 homework problem than a cool riddle... :(

I might have made a mistake somewhere, but I got:
width = 1/4 => height = 1/e

width = x;
height = e[sup]-4x[/sup]
area = x*e[sup]-4x[/sup]

dA/dx = -4x*e[sup]-4x[/sup] + e[sup]-4x[/sup] = e[sup]-4x[/sup](-4x + 1)

e[sup]-4x[/sup](-4x + 1) = 0
(-4x + 1) = 0; e[sup]-4x[/sup] != 0;
-4x = -1
x = 1/4

[quote author=Yoni link=board=36;threadid=7123;start=0#msg63849 date=1086540399]
1/4 x 1/e with an area of 1/4e. Looks more like a calculus 1 homework problem than a cool riddle... :(
[/quote]

way to reply while i was trying to find a calculator to graph it to check my answer.

[quote author=Yoni link=board=36;threadid=7123;start=0#msg63849 date=1086540399]
1/4 x 1/e with an area of 1/4e. Looks more like a calculus 1 homework problem than a cool riddle... :(
[/quote]

Yup, that it is, but I thought you may still get atleast a kick out of it. :)

Not cool enough to be kickworthy imo.