SOLUTION: Find the 2 real numbers whose difference is 12 and whose product is as small as possible. Justify your answer using the 1st or 2nd derivative test. Please explain Thank you

Question 999604: Find the 2 real numbers whose difference is 12 and whose product is as small as possible. Justify your answer using the 1st or 2nd derivative test.
Please explain
Thank you
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
We need to minimize
f(x)=x(12+x)=12x + x^2
Set the derivative equal to zero and get
f'(x) = 12 + 2x = 0
and x = -6
The second derivative is
f''(x) = 2
so you know it is a minimum.
Thus the two numbers are
-6 and 6, and the product is -36.
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