secant line
straight line joining two points on a function
A secant line is a straight line that intersects a curve at two or more points. In calculus, the concept of a secant line is often used to approximate the slope of a curve at a particular point. Specifically, the slope of a secant line passing through two points on a curve can be used to estimate the slope of the curve at the midpoint between those two points.
For example, let’s say we have a curve y=f(x) and we want to estimate the slope of the curve at the point x=a. We can draw a secant line passing through two points on the curve: (a,f(a)) and (a+h,f(a+h)), where h is a small number. The slope of this secant line can be calculated using the formula:
slope = (f(a+h) – f(a))/h
As h gets smaller and smaller, the two points on the curve get closer and closer together, and the secant line becomes a better approximation of the slope of the curve at the point x=a. In the limit as h approaches zero, the two points on the curve become the same point, and the secant line becomes the tangent line to the curve at the point x=a. Therefore, the concept of a secant line is closely related to the concept of a tangent line in calculus.
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