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Question: Implicit differentiation

Question:Implicit differentiation

The function 110 Maple
differentiation implicit
December 29 2022
0

Hello everybody. 

Im working on some implicit differentiation math right now. And by following the example, it is not bringing me anywhere close to the right answer. 

In English it says: Given the implicit written function x^2-2*x*y+2*y^2=12. Determine the local maximum and/or minimum of y and x. 

The answer (as can be seen in the maple file), is for y between 2sqrt3 and -2sqrt3, and -2sqrt6 and 2sqrt6. 

The example clearly states in the solution (oplossing), that the dy/dx needs to be derived for x. But after doing that, and filling in the equation the same way the example is doing it, im not getting to the rigth answer, but -sqrt3/24, and that doesnt look like the right answer


 

> 

#Opdracht 4
> 

x^2-2*x*y+2*y^2-12

x^2-2*x*y+2*y^2-12

 (1)
> 

diff(x^2-2*x*y+2*y^2-12, x)

2*x-2*y

 (2)
> 

diff(x^2-2*x*y+2*y^2-12, y)

-2*x+4*y

 (3)
> 

solve(x^2-2*x^2+2*x^2-12 = 0, x)

2*3^(1/2), -2*3^(1/2)

 (4)
> 

"f(x,y):=x^(2)-2*x*y+2*y^(2)-12"

proc (x, y) options operator, arrow, function_assign; x^2-2*y*x+2*y^2-12 end proc

 (5)
> 

dy/dx = -(2*x-2*y)/(-2*x+4*y)

dy/dx = -(2*x-2*y)/(-2*x+4*y)

 (6)
> 

simplify(%)

dy/dx = (x-y)/(x-2*y)

 (7)
> 

x^2-2*x*y+2*y^2-12
> 

smartplot[x, y](x^2-2*x*y+2*y^2-12 = 0)

 
> 

 

> 

evalf(2*sqrt(3))

3.464101616

 (8)
> 

(x-y)/(x-2*y)
> 

diff((x-y)/(x-2*y), x)

1/(x-2*y)-(x-y)/(x-2*y)^2

 (9)
> 

simplify(%)

-y/(x-2*y)^2

 (10)
> 

-2*sqrt(3)/(2*sqrt(3)*0-(2*2)*sqrt(3))^2

-(1/24)*3^(1/2)

 (11)
> 

evalf(%)

-0.7216878367e-1

 (12)
> 

``

Thank you for your time!

Greetings,

The Function

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