A right triangle has one vertex on the graph of y = 8 - 2x, x > 0 at (x, y), another at the origin, and the third on the positive y-axis at (0,y)

Question

A. Express the area A of the triangle as a function of x.

B. For what value of x is A the largest?

C. What is the maximum area?

Answer 1

A. Area S = x(8 - 2x)/2 = 4x - x²

B. dS/dx = 4 - 2x = 0; x = 2; S'' = - 2 < 0. So at x = 2 we have maximum

C. max S = S(2) = 4