Respuesta :

apologiabiology
verteical is infinite rise/run or when the denomenator of dy/dx is 0

take derivitive, implicit differntation
3x^2+y+x(dy/dx)-2y(dy/dx)=0
3x^2+y=2y(dy/dx)-x(dy/dx)
[tex] \frac{3x^2+y}{2y-x}= \frac{dy}{dx} [/tex]
find when denomenator is equal to 0

2y-x=0
2y=x
solve
subsitute 2y for x
(2y)^3+2y(y)-y^2=10
8y^3+2y^2-y^2=10
8y^3+y^2=10
at aprox y=1.03712
and
2y=x
2(1.03712)=x=2.07424

at about x=2.07424

The value of [tex]x[/tex] would be as follows:

[tex]2.074[/tex]

What is the value of x?

Given that,

Equation:

[tex]x^3+xy-y^2=10[/tex]

As we know,

When [tex]dy/dx = 0,[/tex] the vertical becomes infinite

Through derivative through differentiation,

So,

[tex]3x^2+y+x(dy/dx)-2y(dy/dx)=0[/tex]

[tex]3x^2+y=2y(dy/dx)-x(dy/dx)[/tex]

⇒ [tex](3x^2 + y)/(2y-x) = dy/dx[/tex]

Now, we will determine the situation when the [tex](2y - x)[/tex] [tex]= 0[/tex]

By putting the value [tex]2y[/tex] instead of [tex]x[/tex],

[tex](2y)^3+2y(y)-y^2=10[/tex]

by solving this, we get

[tex]y=1.03712[/tex]

by putting this [tex]y's[/tex] value,

[tex]2y=x[/tex]

[tex]2(1.03712)=x\\=2.074[/tex]

∵ [tex]x = 2.074[/tex]

Learn more about "Tangent Line" here:

brainly.com/question/17060643

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