Math CentralQuandaries & Queries


Question from sundar, a student:

How do I find a normal to a curve defined by equation y = a*x^3+b*x^2+c*x+d


First you need a point on the curve y = f(x) = ax3+bx2+cx+d, let's call it (p, q), then q = f(p). Next you need the slope of the tangent to the curve at (p, q). This slope is the derivative of f(x) evaluated at p, that is the slope is f '(p). The slope of the normal to the curve y = f(x) at x = p is -1/f '(p) and thus the normal to y = f(x) at x = p is the line through (p f(p)) with slope -1/f '(p).


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