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

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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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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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.

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.

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.

- How do you find the equation of the tangent line to the curve #y= (x-3) / (x-4)# at (5,2)?
- What is the equation of the line tangent to # f(x)=2/(4 − x^2)# at # x=3#?
- What is the slope of the line tangent to the graph of #x^2xy+y^2=7#?
- How do you find f'(x) using the limit definition given # f(x)= 2x^2-x#?
- What is the equation of the tangent line of #f(x)=x^3+2x^2-3x+2# at #x=1#?

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