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anonymous
 5 years ago
Maximize Q = xy2, where x and y are positive numbers, such that x + y2 = 4.
anonymous
 5 years ago
Maximize Q = xy2, where x and y are positive numbers, such that x + y2 = 4.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0does y2 means y squared?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If so then the solution of the problem is: You want to maximize Q, that means you need to find the derivative and critical points of Q. The problem here is that Q is in terms of x and y. You should make it in term of only one of them. So we are going to use the second equation to do so. \[x+y^2=4 \implies y^2=4x\] substitute for the value of y^2 into Q, you get: \[Q=xy^2=x(4x)=4xx^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you know how to maximize 4xx^2?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I plug test points into 4xx^2?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the critical number is 4?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you solved for x when the derivative is zero, and you got tgat x=4. this is your only critical point, so it's either maximum or minimum. Which one do you think it is?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the critical point is not x=4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I didn't make it, you did and I didn't see it :P

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Don't worry.. It's so easy. Do you know how to find the derivative of 4xx^2?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Right!! Now solve for x when 42x=0.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now 2 is your critical point, and at x=2 Q is a maximum value.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So now just plug x=2 in Q=4xx^2, and you're done!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What is the maximum value?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0:) I hope you can do any similar problem next time!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks for your help!!
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