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.
- 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?