Question

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=16−x^2. List the dimensions in non-decreasing order.

Answer 1

Since the 2 vertices lying on the parabola, their coordinates will be symmetry over y axis ( x, -x² +16) and ( -x, -x² +16)
-> Length L = 2x, w = -x² +16
=> Area A = 2x ( -x² +16 ) = -2x³ + 32x
=> Max A <=> A' = 0 -> - 6x² + 32 = 0
Thus x = 4 /√3 , A = ...
=

Answer 2

I got x = 2.3094 y = 28.4826