SOLUTION: Consider all the points in the plane that solve the equation x^2 + 2y^2 = 16. Find the maximum value of the product xy on this graph.
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Question 1027081: Consider all the points in the plane that solve the equation x^2 + 2y^2 = 16. Find the maximum value of the product xy on this graph.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
To simplify, the product of would also be a maximum so find the maximum value of .
From the equation,
Substituting,
Find the derivative of ,
Two possible solutions:
This is not a maximum but a local minimum (check with second derivative test).
Then,
So the maximum value would be,
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