## dpflan Find the equation tangent plane to the graph z = (x-4)^2 + (y-4)^2 at p=(5, 6, 5)...? 3 years ago 3 years ago

1. AnwarA

let $f(x,y,z)=(x-4)^2+(y-4)^2-z$ we have the following partial derivatives: $\partial f/\partial x=2x-8$ $\partial f/\partial y=2y-8$ $\partial f/\partial z=-1$ $grad f(x,y,z)= (2x-8)i+(2y-8)j-k$ $grad f(5,6,5)=2i+4j-k$ hence an equation of the tangent line at P(5,6,5) is given by $2(x-5)+4(y-6)-(z-5)=0 \implies 2x+4y-z=29$ hope it's right :)

2. dpflan

Thanks

3. AnwarA

Wow, that was two months ago :D .. You're welcome anyways!!