contestada

A differentiable function f(x,y) has the property that f(3,4)=4 and fx(3,4)=4 and fy(3,4)=−6. Find the equation of the tangent plane at the point on the surface z=f(x,y) where x=3, y=4

Respuesta :

whitneytr12

Answer:

[tex]-4x+6y+z=16[/tex]

Step-by-step explanation:

The equation of the tangent plane to the surface z=f(x,y) in a arbitrary point (x₀,y₀,z₀) is:

[tex]z-z_{0}=f_{x}(x_{0},y_{0})(x-x_{0})+f_{y}(x_{0},y_{0})(y-y_{0})[/tex] (1)

We can define each value using our information:

  • z₀ = f(3,4)=4
  • x₀ = 3
  • y₀ = 4
  • fx(3,4) = 4
  • fy(3,4) = -6

Now, we just need to put these values into the the equation (1)

[tex]z-4=4(x-3)-6(y-4)[/tex]

Simplifying this equation we will have:

[tex]-4x+6y+z=16[/tex]    

I hope it helps you!

Otras preguntas