Question

Find the directional derivative of $f(x, y, z) = -1x^2 + 3y^2 - 3z^2$ at the point $(-1, -4, -3)$ in the direction of the origin.

Name: Find the directional derivative of f(x, y, z) = -1x^2 + 3y^2 - 3z^2 at the point (-1, -4, -3) in the direction of the origin.
Uploaded: 2021-08-21T06:34:19-08:00
Duration: 1 min 26 s
Channel: Linda Hand
Description: Find the directional derivative of f(x, y, z) = -1x^2 + 3y^2 - 3z^2 at the point (-1, -4, -3) in the direction of the origin.

          Find the directional derivative of $f(x, y, z) = -1x^2 + 3y^2 - 3z^2$ at the point $(-1, -4, -3)$ in the direction of the origin.

Added by Kevin H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Linda Hand

08/21/2021

Step 1

The gradient of a function f(x, y, z) is given by the vector ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z). In this case, ∂f/∂x = -2x, ∂f/∂y = 6y, and ∂f/∂z = -6z. So, the gradient of f(x, y, z) is ∇f = (-2x, 6y, -6z). At the point (-1, -4, -3), the gradient is ∇f = (-2(-1), 6(-4), Show more…

Show all steps

Thanks for your feedback!

Find the directional derivative of f(x,y,z)=-1x^(2)+3y^(2)-3z^(2) at the point , -3) in the direction of the origin. Find the directional derivative of f(, y, z) = --1x2 + 3y2 - 3z2 at the point (-1, -4, -3) in the direction of the origin.