 For a double point of "C", the partial derivatives of "f" are all 0 so the first polar contains these points as well.The "class" of "C" may be defined as the number of tangents that may be drawn to "C" from a point not on "C" (counting multiplicities and including imaginary tangents).Each of these tangents touches "C" at one of the points of intersection of "C" and the first polar, and by Bézout's theorem there are at most "n"("n"−1) of these.