secant line
In mathematics, the term “secant line” refers to a straight line that intersects a curve at two distinct points
In mathematics, the term “secant line” refers to a straight line that intersects a curve at two distinct points. More specifically, a secant line intersects a function or curve at two points, creating a line segment between those points.
The secant line is often used in calculus to approximate the slope of a curve at a specific point. By drawing a secant line through two nearby points on a curve, we can estimate the slope of the curve at one of the points.
The slope of the secant line is found using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
This slope represents the average rate of change of the function between the two points.
As the two points on the secant line get closer together, the secant line becomes a better approximation of the tangent line to the curve at a specific point. The tangent line, unlike the secant line, only intersects the curve at one point and represents the instantaneous rate of change or the slope of the curve at that specific point.
The concept of secant lines is widely used in calculus, particularly in determining derivatives and understanding the behavior of functions.
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