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Edited how to test if a graph is a function, to reflect a more accurate definition, including a function of x and a function of y. |
m →Normal to a graph: TeX |
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=== Normal to a graph ===
Given a function ''f'' of ''n'' variables: <math> x=x_1, \
: <math>(\nabla f, -1) </math>
(up to multiplication by a constant). This is seen by considering the graph as a level set of the function <math>g(x,z) = f(x) - z</math>, and using that <math>\nabla g </math> is normal to the level sets.
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