Why this constraint is crucial in a Lagrange multiplier problem?












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Consider we need to find the max. and min. values of this function $ f(x,y)=xy $ subject to the constraint $x^2-y=12$.Why it is necessary to assume that $ yleq0$?










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  • Did you construct the Lagrangian and compute it's derivatives? It should be clear then.
    – Mattos
    Nov 24 at 1:31










  • @Mattos yes i did so and while i am solving, I didnot make use this assumption , but i was wondering why this assumption is stated in the question.
    – John adams
    Nov 24 at 3:06










  • After taking derivatives of the Lagrangian, you should get a condition that $y + 2x^2 = 0$...
    – Mattos
    Nov 25 at 7:06
















0














Consider we need to find the max. and min. values of this function $ f(x,y)=xy $ subject to the constraint $x^2-y=12$.Why it is necessary to assume that $ yleq0$?










share|cite|improve this question
























  • Did you construct the Lagrangian and compute it's derivatives? It should be clear then.
    – Mattos
    Nov 24 at 1:31










  • @Mattos yes i did so and while i am solving, I didnot make use this assumption , but i was wondering why this assumption is stated in the question.
    – John adams
    Nov 24 at 3:06










  • After taking derivatives of the Lagrangian, you should get a condition that $y + 2x^2 = 0$...
    – Mattos
    Nov 25 at 7:06














0












0








0







Consider we need to find the max. and min. values of this function $ f(x,y)=xy $ subject to the constraint $x^2-y=12$.Why it is necessary to assume that $ yleq0$?










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Consider we need to find the max. and min. values of this function $ f(x,y)=xy $ subject to the constraint $x^2-y=12$.Why it is necessary to assume that $ yleq0$?







lagrange-multiplier






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share|cite|improve this question













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edited Nov 24 at 1:27









Bernard

118k639111




118k639111










asked Nov 24 at 1:19









John adams

206




206












  • Did you construct the Lagrangian and compute it's derivatives? It should be clear then.
    – Mattos
    Nov 24 at 1:31










  • @Mattos yes i did so and while i am solving, I didnot make use this assumption , but i was wondering why this assumption is stated in the question.
    – John adams
    Nov 24 at 3:06










  • After taking derivatives of the Lagrangian, you should get a condition that $y + 2x^2 = 0$...
    – Mattos
    Nov 25 at 7:06


















  • Did you construct the Lagrangian and compute it's derivatives? It should be clear then.
    – Mattos
    Nov 24 at 1:31










  • @Mattos yes i did so and while i am solving, I didnot make use this assumption , but i was wondering why this assumption is stated in the question.
    – John adams
    Nov 24 at 3:06










  • After taking derivatives of the Lagrangian, you should get a condition that $y + 2x^2 = 0$...
    – Mattos
    Nov 25 at 7:06
















Did you construct the Lagrangian and compute it's derivatives? It should be clear then.
– Mattos
Nov 24 at 1:31




Did you construct the Lagrangian and compute it's derivatives? It should be clear then.
– Mattos
Nov 24 at 1:31












@Mattos yes i did so and while i am solving, I didnot make use this assumption , but i was wondering why this assumption is stated in the question.
– John adams
Nov 24 at 3:06




@Mattos yes i did so and while i am solving, I didnot make use this assumption , but i was wondering why this assumption is stated in the question.
– John adams
Nov 24 at 3:06












After taking derivatives of the Lagrangian, you should get a condition that $y + 2x^2 = 0$...
– Mattos
Nov 25 at 7:06




After taking derivatives of the Lagrangian, you should get a condition that $y + 2x^2 = 0$...
– Mattos
Nov 25 at 7:06















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