Example 4-5-1 - Maple Help

# Online Help

###### All Products    Maple    MapleSim



Chapter 4: Partial Differentiation



Section 4.5: Gradient Vector



Example 4.5.1



Let  and let P be the point $\left(1,2\right)$.

 a) Obtain $\nabla f$ at P.
 b) Graph the surface $z=f\left(x,y\right)$.
 c) On the same set of axes, graph the level curve through P, and $\nabla f$ at P.
 d) At P, show that $\nabla f$ is orthogonal to a vector tangent to the level curve through P.
 e) At P, obtain $\mathrm{ψ}=\left(\nabla f\right)·\mathbf{u}$, the directional derivative of $f$ in the direction  . Show that $\mathrm{ψ}$ is a maximum when u is along $\nabla f\left(\mathrm{P}\right)$ and that this maximum is $∥\nabla f\left(\mathrm{P}\right)∥$.







© Maplesoft, a division of Waterloo Maple Inc., 2021. 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