By: Zach HuyberPeriod 4

AP Calculus

Tangent Lines

What is a Tangent Line?

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

Tangent line compared to Secant Line

• A Tangent line touches the curve at just one point unlike a secant line which touches the graph at two points

• The slope of a tangent line is a instantaneous slope at one point and a secant lines slope is a approximation or sort of a line of best fit.

Why do we need Tangent lines?

• We use tangent lines to find the slope of a graph at one particular point in order to get that points instantaneous velocity or acceleration.

Vertical Tangent Line

• A vertical tangent line is a line with a infinite or undefined slope, therefore this is an indication of a point that is not differentiable

Not Differentiable

How to Find a Tangent Line at a given point

Example #1

For work and answers refer to PowerPoint problems explained document on powerpoint page

Example #2

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Example #3

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Example #4

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Example #5

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Good LuckOWN IT!!!!!