a rectangle has one corner in quadrant 1 on the graph of y=16-x squared, another at the origin, and a third on the positive y-axis, and the fourth at the positi

Question

a rectangle has one corner in quadrant 1 on the graph of y=16-x squared, another at the origin, and a third on the positive y-axis, and the fourth at the positive x-axis.(a) express the area a of the rectangle as a function of x.(b) what is the domain of A?(c) graph A=A(x). for what value of x is A largest?

Answer 1

a) A = xy = x(16-x^2)

b) Domain: (0, 4)

c) A' = 0 => 16-x^2-2x^2 = 0 => x = 4/sqrt(3) gives the largest A = 24.6 units^2

Or you can graph it, and find maximum A at x = 2.3094.