Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

LeoMessi

  • 3 years ago

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

  • This Question is Closed
  1. Owlfred
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 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. dpflan
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 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

  3. fauxshaux
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    dw= dz + dx + dy

  4. azumih
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 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...

  5. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.