Question

A rectangle has one side on the x-axis, one side on the y-axis, one vertex at the orgin ans one on the curve y = e^-3x , for x>(equal) 0. find the maximum area (using calculus)

Answer 1

a = xy = xe^(-3x)
da/dx = (1-3x)e^(-3x)

so, where is da/dx = 0?

Answer 2

is the answer 3?

Answer 3

no.
e^(-3x) is never zero, so where is (1-3x)=0?

x = 1/3

so, a = (1/3)e^(-3*1/3) = 1/(3e)

don't forget your Algebra I now that you're in Calculus!