What is the minimum product of two numbers whose difference is 30?

Let's call the two number and . Since we know that the difference between them is , if we assume to be the largest we have

Their product is , which we can write as

This is the equation of a parabola, since it is a polynomial of degree . To find its minimum, simply derive it and set the derivative to zero: using the power rule

we have the following derivative:

Now that we have found one variable, we can substitute its value in the formula that related it to the other variable:

So, the two numbers are and

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If gravity is one third on mars then weight also one third on mars