Find the tangent plane given at the stationary point.

[Jozefina Gramatikova]

Homework Statement

Homework Equations

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The Attempt at a Solution

I got -1, but the answer says "6". Could you help me, please?

 

[verty]

I see a mistake in the x-partial. You have not substituted in correctly.

 

[Jozefina Gramatikova]

I see a mistake in the x-partial. You have not substituted in correctly.

Oh, thanks! But then 3-3=0 and the whole thing is 0

 

[verty]

So what do you think the tangent plane looks like? And what is its formula?

PS. This is all the help I can give, sorry.

 

[tnich]

Oh, thanks! But then 3-3=0 and the whole thing is 0

In the relevant equations, you have correctly given the equation of a plane. You can rewrite this as
$(a, b, c) \cdot (x-x_0,y-y_0,z-z_0) = 0$

This says that $(a, b, c)$ is normal to all of the vectors in the plane.

If this plane is tangent to the surface described by $(x, y,f(x,y))$ at $(x_0,y_0,z_0)$, then $(a, b, c)$ would also have to be normal to that surface at that point. How would you find the vector $(a, b, c)$ that is normal to the surface?