Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola y=6-x² . Width = Height =

Answer 1

Draw a diagram. Let P be the upper right corner of the rectangle. P = (x, 6 - x²)

The rectangle has base 2x and height 6 - x².

A = area of rectangle = 2x(6 - x²) = 12x - 2x³

A' = 12 - 6x²

A' = 0 when x = √2. Show that this value of x maximizes A.

Answer 2

x= sqr2 = about 1.414

but times two for the base = 2sqr2 = 2.828

y = height = 6-x^2 = 6-2= 4