Another riddle!

[Raven]

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?

[Yoni]

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

[K]

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

width = x;
height = e^-4x
area = x*e^-4x

dA/dx = -4x*e^-4x + e^-4x = e^-4x(-4x + 1)

e^-4x(-4x + 1) = 0
(-4x + 1) = 0; e^-4x != 0;
-4x = -1
x = 1/4

[K]

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

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

[Raven]

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

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

[Yoni]

Not cool enough to be kickworthy imo.