SOLUTION: The sum of two numbers is 20. Find the numbers and their product if their product is a maximum

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Question 1128390: The sum of two numbers is 20. Find the numbers and their product if their product is a maximum
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+highlight%28+10+%29+ and +highlight%28+10+%29+
Product = +highlight%28+100+%29+
——
Workout:
A+B = 20
P = AB = A(20-A)
dP/dA = 20-2A
dP/dA = 0 = 20 - 2A —> A=10 —> B=10
d%5E2P%2FdA%5E2+=+-2++ so the function is concave down and the value found above for A is maximal.