Sum of two numbers is 24.find numbers if product is maximum

Solution

Let one number is x and other is 24-x

X(24-x)should be maximum

24x-x^2 Derivative of this function is

24-2x

X=12

Again second derivative =-2

By second derivative test it should be maximum

At x=12 so other will be also 12

It satisfied condition that the product is maximum