a rectangle is inscribed under the curve y=e^(-x)^2, with its base along the x-axis. Find the rectangle of largest area, subject to the restriction that the base does not exceed 4 units.
Now I want to maximize the area of the rectangle, so should I do this?
A=xy
=[e^(-x)^2]x
Tested the domain
f(0)=1
f(4)=0.0000000112
now this doesn't make much sense because we dont have a rectangle if the largest area is 1..... x =0? not rectangle.
Please guide me to enlightenment! really appreciate it. thank you
Hi skeske1234
If you draw the graph of , it will be on 1st and 2nd quadrant and is symmetry about y-axis. So, the rectangle will also lie on 1st and 2nd quadrant and is symmetry about y-axis.
A = xy is only the area on one quadrant. If you take positive value of x, then the rectangle is on 1st quadrant. If you take negative value of x, the rectangle is on 2nd quadrant.
Hence, to get the total area : A = 2xy
Maybe, it will be clearer if someone posts the graph
Have a look here: http://www.mathhelpforum.com/math-he...oblem-2-a.html