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

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