Find the dimensions of the rectangle of maximum area bounded

Solution

if f(x) = (6 - x) / 2 the area could be said to be - A = x f(x) giving the function: Area = (6x - x^2) / 2 if A = (6x - x^2) / 2 = 3x - ((x^2)/2) Differentiate - dA / dx = 3 - x The stationary point (either max or min) is where dA / dx = 0 1 - x = 0 so at x = 1 there is either a maximum or minimum. The dimensions of maximum area are 1 and f(1), i.e. f(1) = 5/2 so the rectangle of maximum area has dimensions: (1) X (5/2)