# The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible.

What does it mean? This is from applications of derivatives. How do I solve this.

Two numbers, x, and 20-x

Sumsquares= x^2 + (20-x)^2 is max.
Take the derivative of this, set to zero, solve for x, and 20-x. You should get two solutions, one is a max, one is a min.

I get x=10, means the numbers are 10 and 10.

At the back of the book , answers are:
as large as possible 0,20
as small as possible 10,10

How do we get the second solution? that is 0 and 20

Jen, I have a problem with the answer. The problem was stated as two positive numbers. Zero is not a positive number, positive numbers are greater than zero.

Now, your question. You can not use the derivative except to find where the slope is zero (max or min). Therefore, the other solution has to be tested at at the endpoints in the original function. The slope is not zero at zero, or x=20.

we have a similar problem, except the questions asks for "nonnegative numbers" which will get you the answers that are at the back of the book.

perhaps just a miscommunications on the book's or Jen's part?

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