If x is required to be positive, you are correct, though you need to show that the rectangle does not become larger as you go to 0 or . If x can be negative, the retangle can be arbitrarily large.
find the maximun are of rectangle if his points are O(0,0) A (x,0) C(0,y) and B is in the graph of function
i tried this way:
S= x * y = x * e^(-x)
then i found the first derivative, then found the point wich the funcion has extremum (x=1) then i found the second derivative and pluged the extrem point x=1 into the function witch was now <0
now the maximum area is S=1*e^(-1)
am i right ? if isn't how should i solve this ?