A rectangle is made having 1 side on the x-axis and the 2 upper corner points on the graph of y = 4e^(−2x^2)+3). Determine the max. possible area, Amax, of this.

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The rectangle will have width 2x and height `4e^(-2x^2+3)` . (Note that the given function is symmetric about the y-axis.)

The area will be `A=(2x)(4e^(-2x^2+3))=8xe^(-2x^2+3)`

To maximize this function we take the first derivative...

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