Optimization

[slynnie90]

A rectangle is constructed with one side on the positive x-axis, one side on the positive y-axis, and the vetex opposite the origin on the line y=10-2x. What are the dimension of the rectangle of maximum area, and what is the area?


I have everything up through A'(x)=10-4x

x=2.5, I do not know where to go from here, however! Any help would be appreciated!

 

[srmichael]

Congratulations! You did the hard part...finding the equation to optimize, taking the derivative and then solving for the variable. You have x = 2.5, so that is one side of the rectangle. Plug this into y=10-2x to get y, the other side then plug in x=2.5 into the area formula to get the area. Make sense?