Question

Optimization fun :D

Answer 1

A rectangle has one side on the x-axis, one side on the y-axis, one vertex at the origin and one on the curve:
\[y=e^{-2x}\] for \[x\ge 0\]
Find the :
a.) Maximum area
b.) Minimum perimeter

Answer 2

Formualte your P and A functions...

Answer 3

Maximize
Area = length * width = x*y = x*e^(-2x)

Answer 4

\[\frac{ dA }{ dx }=(1-2x)e^{-2x}\]

that is zero when x=1/2

Answer 5

that is a maximum value, dA/dt is positive to the left and negative to the right of x=1/2