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

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.

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asked by Betty
  1. x e^x is concave up for x > -2

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

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    posted by Steve
  2. my function is xe^(-x).

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    posted by Betty
  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)

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    posted by Steve

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