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What is the difference between a Tangent line and a secant line on a curve?

Answer 1

The tangent line to a curve at a given point is a straight line that just "touches" the curve at that point.

So if the function is f(x) and if the tangent "touches" its curve at x=c, then the tangent will pass through the point (c,f(c)). The slope of this tangent line is f'(c) ( the derivative of the function f(x) at x=c).

A secant line is one which intersects a curve at two points.

Click this link for a detailed explanation on how calculus uses the properties of these two lines to define the derivative of a function at a point.

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Answer 2

Emilia Aguilar

A tangent line touches a curve at a single point, while a secant line intersects a curve at two or more points.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.