Find the area a of the largest rectangle that can be inscribed under the curve of the equation below in the first and second quadrants.
y = e^−x^2

F(x) = f(-x)

If the point on the curve (x,y) is in the first quadrant,the opposite corner of the rectangle will be (-x,y). 

So,
f(x) = 2 x y
        = e^(-x^2)
f'(x) = d/d x [e^−x^2] 
       = e^−x^2⋅d/dx [−x^2]       =(−d/d x [x^2])e^−x^2       =−2 x e^−x^2
       = x (-2 e^-x)
f'(x) = 0
where x = 0 
So, x = 0
we only want the positive, real root here 

f(0) = e^(-0)
      = 1

30 degrees

Step-by-step explanation: