1. Copyright © 2013 All rights reserved, Government of Newfoundland and Labrador Calculus 3208 Derivative (22) Unit 4: Chapter # 2 – Section 2.1 (Essential Calculus) Equations of Tangent and Normal Lines

2. Copyright © 2013 All rights reserved, Government of Newfoundland and Labrador Equations of Tangent and Normal Lines Review of Linear Functions and Properties Finding the Equation of a Tangent Line Finding the Equation of a Normal Line

3. Copyright © 2013 All rights reserved, Government of Newfoundland and Labrador Review of Linear Functions and Properties Slope of a Line: The following information about linear functions was covered in Math 1201, and is useful again here. Slope-Intercept Form of the Equation of a Line: Slope-Point Form of the Equation of a Line: Parallel Lines: Perpendicular Lines:

4. Copyright © 2013 All rights reserved, Government of Newfoundland and Labrador Tangent and Normal Lines Point of Tangency

5. Copyright © 2013 All rights reserved, Government of Newfoundland and Labrador The Equation of a Tangent Line In Slope-Point Form: To find the equation of the line tangent to a function at the point where Our Goal: Equation of Tangent Line:

6. Copyright © 2013 All rights reserved, Government of Newfoundland and Labrador The Equation of a Normal Line In Slope-Point Form: To find the equation of the line tangent to a function at the point where Our Goal: Equation of Tangent Line:

7. Copyright © 2013 All rights reserved, Government of Newfoundland and Labrador Find the equations of the normal and tangent lines that touch the curve at the point where

8. Copyright © 2013 All rights reserved, Government of Newfoundland and Labrador Find the equations of the normal and tangent lines that touch the curve at the point where

9. Copyright © 2013 All rights reserved, Government of Newfoundland and Labrador Find the equations of the normal and tangent lines that touch the curve at the point where - Solution Point of Tangency Derivative Slope of Tangent Slope of Normal Equation of Tangent Equation of Normal

10. Copyright © 2013 All rights reserved, Government of Newfoundland and Labrador There are two important things to know in order to get the equation of a tangent or a normal; the point of tangency (a, f(a), and the value of the derivative f’(a). The equation of the normal line is found using: The equation of the tangent line is found using: