Tangent lines touch a curve at a single point and have a slope that represents the curve's instantaneous rate of change at that point, unlike secant lines which pass through two points on a curve. We use tangent lines to find velocity or acceleration at a specific point on a graph. A vertical tangent line has an undefined slope, indicating a non-differentiable point. The document provides examples of finding tangent lines at given points on graphs.

1. By: Zach Huyber Period 4 AP Calculus Tangent Lines

2. 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

3. 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.

4. 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.

5. 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

6. How to Find a Tangent Line at a given point

7. Example #1

8. Example #2

9. Example #3

10. Example #4

11. Example #5

12. Good Luck OWN IT!!!!!