SOLUTION: How can I find the answer to this? Find two positive numbers' largest product if the first number plus twice the second number is equal to 48. I think I am supposed to use the firs
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Question 677368: How can I find the answer to this? Find two positive numbers' largest product if the first number plus twice the second number is equal to 48. I think I am supposed to use the first and second derivatives, but I'm not sure how to set it up!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
represent the first number, and 
represent the second number, then
Hence, 
So \ =\ -(2p_2)^2\ -\ 48p_2)
Take the first derivative, set it equal to zero. Solve to get the ordinate of the extreme point.
Take the second derivative and evaluate it at the ordinate of the extreme point. If positive, the extreme is a minimum, if negative, the extreme is a maximum.
John
My calculator said it, I believe it, that settles it
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