Chapter 4: Partial Differentiation
Section 4.6: Surface Normal and Tangent Plane
Table 4.6.1 lists expressions for a vector N, normal to a surface defined either explicitly by and equation of the form z=fx,y; or implicitly, by an equation of the form fx,y,z=c, where c is a real constant.
Surface defined explicitly
Surface defined implicitly
Table 4.6.1 Surface normals for surfaces defined explicitly and implicitly
If the gradient ∇f is normal to the level surface defined implicitly by an equation of the form fx,y,z=c, then writing the equation z=fx,y for the explicitly given surface in the implicit form z−fx,y=0, leads to the surface normal
At P:2,−3 on the surface defined by z=fx,y≡5−x2/3−y2/2, obtain and draw both the normal and tangent plane.
At P:a,b on the surface defined by z=fx,y, obtain an equation for the tangent plane in the form z=….
Derive the form of N for the surface given explicitly by z=fx,y. (See Table 4.6.1.)
At P:1,1,1 on the surface defined by fx,y,z≡x2+2 y2+3 z2=6, obtain and draw both the normal and tangent plane.
At P:a,b,c on the surface defined implicitly by fx,y,z=0, obtain an equation for the tangent plane in the form z=….
Derive the form of N for the surface given implicitly by fx,y,z=c, where c is a real constant. (See Table 4.6.1.)
<< Previous Section Table of Contents Next Section >>
© Maplesoft, a division of Waterloo Maple Inc., 2023. 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