Illustration of Level Set and Gradient
Here f(x,y) = x2 + y2, and the paraboloid (blue surface) is the graph of f. We consider the level set Lf(3) of f at level 3. It is a circle in R2. The point a is a solution of the level set equation
f(x,y) = x2 + y2 = 3.
A level set of the derivative f '(a) is the (blue) tangent plane to the circle Lf(3) at the point a.
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