Secants and Tangents

A secant line of a curve is a line that (locally) intersects two points on the curve. The word secant comes from the Latin secare, to cut.

It can be used to approximate the tangent to a curve, at some point P. If the secant to a curve is defined by two points, P and Q, with P fixed and Q variable, as Q approaches P along the curve, the direction of the secant approaches that of the tangent at P, (assuming that the first-derivative of the curve is continuous at point P so that there is only one tangent). As a consequence, one could say that the limit as Q approaches P of the secant’s slope, or direction, is that of the tangent. In calculus, this idea is the basis of the geometric definition of the derivative. A chord is the portion of a secant that lies within the curve. Read more on Wikipedia
In geometry, the tangent line (or simply the tangent) to a plane curve at a given point is the straight line that “just touches” the curve at that point. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c on the curve if the line passes through the point (c, f(c)) on the curve and has slope f’(c) where f’ is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space. Read more on Wikipedia

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