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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  • rotchm
    Lv 7
    4 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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