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# Calculus 1 Homework Question?

Find two positive numbers that satisfy the given requirements. The sum of the first number squared and the second number is 54 and the product is a maximum.

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- rotchmLv 74 weeks ago
Starting it is all highschool math:

Let x & y be your numbers. You are told that: x² + y = 54. The product P = x*y. Isolating y in the above and replacing in P gives:

P = x² * (54 - x² ). Expanding gives P = 54x² - x^4.

Now the calculus part. An optimal value may be found via P' = 0.

So differentiate P = 54x² - x^4. What do you get?

Now solve for = 0. What do you get for x ?

Can you take it from there?

Done!

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