Big Picture / We are beginning our Calculus Unit. In our first look at Calculus we must begin where it all began…with Limits. This will eventually lead us into the derivative. Once we have developed the Derivative we must delve into more complex functions and applications of Derivatives.
Context of this Lessons / We move from the rules of derivatives into working with Tangent and Normal lines. This topic can be a bit tricky so please make sure to try some of them out!
To Do Today!
IB SL 2 - Lesson 9.4: Tangent and Normal Lines / Unit 9: Calculus-Task 0:L
-Task 1:Questions from HW
-Task 2:Derivative Practice
-Task 3:Tangent and Normal Lines
-Task 4: IB Problems # 4 and Book Work
-Pg. 207 7G 1, 2ad, 3a, 4, 5
Task 0: Please evaluate the following limits. Please open their graphs on Desmos for the visual.
Task 1: HW/IB Problem Discussion
Task 2: Derivative Practice
Further Examples: Differentiate each function below
Basic:
Task 3: Tangent and Normal Lines
Tangent Line: At a point (x,y) Line that “touches” the function at a single point. This line represents the instantaneous rate of change at that point (x,y).
Normal Line: the Normal line at a point (x,y) on a curve is the line perpendicular to the tangent line at that point (x,y).
Remember: To find the equation of a line you need what two things?
- Find the lines that are tangent and normal to the following curves at the given values of x.
- Find the points on the given function where the tangent line is parallel to the x axis.
- Find the equation of the normal line to the given function at the point (2,3).
- Find the equation of the normal line to the given function, that is parallel to the line y = 1/3 x + 7.
- Find the area of the triangle that is formed by the line tangent to the function at x = -2 and the line x=0 and y=-4. Draw a picture to help.
Task 4: IB Problems # 4