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Question: An example of a math book, but is sure does not reveal how it got the answer

Question:An example of a math book, but is sure does not reveal how it got the answer

The function 110 Maple
optimization calculus maximum
January 05 2023
0

Hello everybody! Happy new year!

Allright, well, the question states the following: "What is the maximum product of the fromula x*y*z which has the sum of 6 if you add x, y, and z together".

Now, i am seeing what they are doing, but somewhere down the line in the explaination they say "(after some calculations)". 

Isnt there a faster way to do it? And what did they do in the example to get to the result?

Thank you very much!

Greetings,

The Function    

> 

solve(x+y+z = 6, z)

6-x-y

 (1)
> 

x*y*(6-x-y)

x*y*(6-x-y)

 (2)
> 

expand(x*y*(6-x-y))

-x^2*y-x*y^2+6*x*y

 (3)
> 

diff(-x^2*y-x*y^2+6*x*y, x)

-2*x*y-y^2+6*y

 (4)
> 

convert(-2*x*y-y^2+6*y, 'horner', y)

(-2*x+6-y)*y

 (5)
> 

solve(-2*x*y-y^2+6*y = 0, y)

0, -2*x+6

 (6)
> 

y := 0; solve(-2*y+6 = x, x)

0

  

6

 (7)
> 

restart
> 

diff(-x^2*y-x*y^2+6*x*y, y)

-x^2-2*x*y+6*x

 (8)
> 

convert(-x^2-2*x*y+6*x, 'horner', x)

(-2*y+6-x)*x

 (9)
> 

solve(-x^2-2*x*y+6*x, x)

0, -2*y+6

 (10)
> 

x := 0; solve(-2*x+6 = y, y)

0

  

6

 (11)
> 

``

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