Calculus › Section N · Functions of several variables › Topic N.7
Tangent planes and normal lines
A curve has a tangent line; a surface deserves a tangent plane. This topic finds that plane, the normal line perpendicular to it, and the gradient's starring role as the normal direction.
In this topic
- From tangent lines to tangent planes
- The tangent plane to a graph
- Worked example: a paraboloid
- Level surfaces and the gradient
- Why the gradient is normal
- Worked example: a sphere
- The normal line to a graph
- The tangent plane as an approximation
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP