Chapter 4: Partial Differentiation
Section 4.5: Gradient Vector
Example 4.5.3
Prove Property 1 in Table 4.5.1.
Solution
Property 1: The gradients of are orthogonal to the level curves defined implicitly by , where is a real constant.
Represent the level curve in the position-vector form so a vector tangent to this curve is then .
By implicitly differentiating to get , the derivative is obtained.
Hence, the tangent vector is , and = .
The gradient is therefore orthogonal to the level curve defined implicitly by .
<< Previous Example Section 4.5 Next Example >>
© Maplesoft, a division of Waterloo Maple Inc., 2024. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com
Download Help Document