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# Consider the following: Find two numbers whose sum is $23$ and whose product is a maximum.(a) Make a table of values, like the one at the right, so that the numbers in the first two columns is always $23$. On the basis of the evidence in your table, estimate the answer to the problem.(b) Use calculus to solve the problem and compare with your answer to part (a).

## $0=23-24, n=11 . 5$

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

Okay. Table of values. First number one. Number two would be 22. Product is 22. Keep doing this. Three times, 20th 60 four terms. 19. So now that we get this, we know that if we continue onwards, until we get to 12 times 11 we end up with the 132. We know this is gonna be the maximum product. Therefore, we know the maximum value would be, which means writing in terms of, um we get 23 months on 23 minus on dsquared. Therefore the derivative minus two and 23 minutes to end. So we get zero equals 23 minus two on they're for an is 23 over two, which is 11.5, So the maximum value is 11.5. And remember, we got 11 and 12 is our two numbers.

#### Topics

Derivatives

Differentiation

Volume

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp