Question

Determine the largest area of the rectangle whose base is on the x-axis and the two vertices lie on the curve y-e^-x^2

Answer 1

Answer:

Step-by-step explanation:

1

Let's t1 and t2 the abscissas of the lower vertices (t2>t1) and clearly the upper vertices have the ordinates

12−t21=12−t22⟺t1=−t2sincet1≠t2

and the area of the rectangle is

(t2−t1)(12−t21)=2t2(12−t22)

hence to answer the question we should maximize the function

f(t)=t(12−t2)

and since

f′(t)=12−t2−2t2=12−3t2=0⟺t=±2

hence we see easily that t2=2 and the area is

2f(2)=32