Find the maximum value of (x^2)(y^3)

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Find the maximum value of (x^2)(y^3) | algebra | AM-GM relation

3x + 4y = 5 (x,y are positive)
Greatest value of (x^2)(y^3) = ?

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This is a very easy ques easily solved by lagrange multiplier

imranfarhad

Good clear solution. Ur real mathematician. Cleat voice...

vuyyurisatyasrinivasarao

I substituted x=(5-4y)/3 and then plugged it into x²y³ and took the first and second derivative test to find critical points and then got same answer

brinzanalexandru

Not familiar with the AM-GM method. I will have to do some research on that. I solved it using calculus and setting derivative equal to zero.

covenslayer

max when x= 2/3, y= 3/4 , so max of the expression is 3/16

strikerstone

Not sure the problem is solved in the video. Only an upper bound is provided.
Why is the maximum value attained? One should give the values for x and y that x^2y^3=3/16 so that the inequality is not always a strict inequality.

On peut pas dire que 3/16 est max que si on trouve les valeur de x et y .c est déjà signalée dans les commentaires. Supposant qu’on prendre pour décomposition x+2x+y+y+2yon va trouver que x^2y^3<=1/4 .et bien sur ce nombre n est pas le maximum.car dans le cas de Max les nombre sont égale

abdeljalilerraissi

I solved a similar question a couple of days ago. It said x²y³=6, find out the maximum value of 3x+4y.

ankitbhattacharjee_iitkgp

GM is greatest when all terms are equal. The gif shows a geometric proof, and the Wikipedia article discusses it.

aliksegal

The left side in the AM>GM is set so that it gives the 5 for the nominator, but how does the right side work? Just from AM-GM...
The result looks correct.

jarikosonen

It seems that (standard) derivative calculation yields the extreme points of x, so that the maximum of the target function.

michaelsadovsky

How can I find the minimum value of x²y³?

pratyushdutta

Why you are making gaming this sum

Just apply maxima minima in calculus.

You may say to me what is the problem?

Yes

But apply this method as a second or auxiliary method

susennath

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