Calculus 14.4 Tangent Planes and Linear Approximations

My notes are available at asherbroberts.com/ (so you can write along with me).
Calculus: Early Transcendentals 8th Edition by James Stewart

[@thomash9008]

Maybe I'm dumb, but your remarks around 14.4.4 have clarified things for me, thank you sir.

[@JC-qf2yg]

THANKS!

[@kuntayyılmaz]

Question at 11.00 after you take partial derivatives instead of putting (1,0) to both derivatives you puth (0,1) that is not mistake rigth not intended?

[@asherroberts]

Yes, I made a mistake there.