Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Find the equation tangent plane to the graph z = (x4)^2 + (y4)^2 at p=(5, 6, 5)...?
 2 years ago
 2 years ago
Find the equation tangent plane to the graph z = (x4)^2 + (y4)^2 at p=(5, 6, 5)...?
 2 years ago
 2 years ago

This Question is Closed

OwlfredBest ResponseYou've already chosen the best response.0
Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!
 2 years ago

dpflanBest ResponseYou've already chosen the best response.0
All rright, here we go! let f(x,y,z)=(x−4)2+(y−4)2−z we have the following partial derivatives: ∂f/∂x=2x−8 ∂f/∂y=2y−8 ∂f/∂z=−1 gradf(x,y,z)=(2x−8)i+(2y−8)j−k gradf(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⟹2x+4y−z=29
 2 years ago

azumihBest ResponseYou've already chosen the best response.0
\[\partial{z}/\partial{x}_5 = 2(x  4)_5 = 2\] \[\partial{z}/\partial{y}_6 = 2(y  4)_6 = 4\] Hence the tangent plane has gradient (2, 4). Its equation is in the form \[z = 2x + 4y + p\] And it passes through (5, 6, 5), so \[5 = 2*5 + 4*6 + p\] \[p = 29\] Result: \[z = 2x + 4y  28\] How about that...
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.