Problem - Use calculus to find the dimension (base and height) and the area of the largest rectangle that can be inscribed in the ellipse x2/144 + y2/16 = 1.
(a) Inscribed rectangle has dimensions base = 2x, height = 2y → area is A = (2x)(2y).
(b) Solve the equation for the ellipse for y in terms of x. Use the positive √ only.
(c) Write area as function A of c only and find the critical number of A(x) that maximizes area.
(d) Warning: √(a-b) ≠ √a - √b, so that x/12 + y/4 = 1 is unrelated to this problem!
