# use calculus optimization techniques to find two numbers whose products is 147 and the sum of the first number plus the second number is a minimum?

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justaguide | Certified Educator

The product of the two numbers to be found is 147 and the sum of the two numbers should be a minimum. Let the first number be X, the second number is 147/X

The sum of the numbers is S = X + 147/X

To minimize S, S' = 0 has to be solved.

=> 1 - 147/X^2 = 0

=> 147 = X^2

=> X = `sqrt(147)`

**The product of the the two numbers is 147 and their sum is a minimum when the numbers are both equal to `sqrt 147` **