Question

If the gradient of $f$ is $\nabla f = y\vec{j} - 3x\vec{i} - zy\vec{k}$ and the point $P = (-1, -3, 8)$ lies on the level surface $f(x, y, z) = 0$, find an equation for the tangent plane to the surface at the point $P$. $z = x - y + 8z - 66 = 0$

Name: if the gradient of f is nabla f yvecj 3xveci zyveck and the point p 1 3 8 lies on the level surface fx y z 0 find an equation for the tangent plane to the surface at the point p z x y 8z 66 30573
Uploaded: 2023-07-25T22:36:49-08:00
Duration: 2 min 25 s
Channel: Madhur L
Description: if the gradient of f is nabla f yvecj 3xveci zyveck and the point p 1 3 8 lies on the level surface fx y z 0 find an equation for the tangent plane to the surface at the point p z x y 8z 66 30573

          If the gradient of $f$ is $\nabla f = y\vec{j} - 3x\vec{i} - zy\vec{k}$ and the point $P = (-1, -3, 8)$ lies on the level surface $f(x, y, z) = 0$, find an equation for the tangent plane to the surface at the point $P$.
$z = x - y + 8z - 66 = 0$

if the gradient of f is nabla f yvecj 3xveci zyveck and the point p 1 3 8 lies on the level surface fx y z 0 find an equation for the tangent plane to the surface at the point p z x y 8z 66 30573

Added by Jessica B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/25/2023

Step 1

Step 1: The gradient of $f$ at point $P$ is given by: $\nabla f(-1, -3, 8) = (-3)\vec{j} - 3(-1)\vec{i} - (8)(-3)\vec{k} = 3\vec{i} - 3\vec{j} + 24\vec{k}$ This vector is normal to the tangent plane at point $P$. Show more…

Show all steps

Thanks for your feedback!

If the gradient of $f$ is $\nabla f = y\vec{j} - 3x\vec{i} - zy\vec{k}$ and the point $P = (-1, -3, 8)$ lies on the level surface $f(x, y, z) = 0$, find an equation for the tangent plane to the surface at the point $P$. $z = x - y + 8z - 66 = 0$