Given two numbers x and y such that:
x + y = 12 ... (1)
two numbers will maximize the product gfrom equation (1)
y = 12 - x Using this value of y, we represent xy asxy = f(x)= x(12 - x) f(x) = 12x - x^2Differentiating the above function:f'(x) = 12 - 2xMaximum value of f(x) occurs at point for which f'(x) = 0.Equating f'(x) to 0 we get:12 - 2x = 0 2x = 12> x = 12/2 = 6Substituting this value of x in equation (2):y = 12 - 6 = 6Therefore, value of xy is maximum when:x = 6 and y = 6The maximum value of xy = 6*6 = 36