Question

The figure shows the graph of f(x)=xe^x, x greater than or equal to 0.

figure: f(x) curve is drawn and under the max. point/ concave down curve there is an inscribed rectangle. with width from a(left) to b(right) and height up to a certain point of f(x).

Let a > 0 and b > 0 be given as shown in the figure. Complete the following table where A is the area of the rectangle in the figure.

a b A
0.1
0.2
0.3
.
.
.
1

I have no idea how to fill in b and A columns. The answer starts with b as 3.71 and A as 0.33, which I don't understand because a*b in this case does not give 0.33.

Answer 1

x e^x is concave up for x > -2

I don't see how your description can be right.

Answer 2

my function is xe^(-x).

Answer 3

If a = 0.1, f(a) = 0.09048
Draw that horizontal line, and it intersects the curve at b=3.71495
Thus, A = 0.09038(3.71495-0.1) = 0.32672

Do the others the same way:
find f(a)
see where else f(b) = f(a)
calculate A = f(a)*(b-a)