1. When does a derivative not exist?
Differentiability
When does a derivative not exist?

2. Polynomial: Derivative exists everywhere

3. Three reasons a derivative does not exist
Function
Not Continuous

4. 2. Vertical Tangent

5. 3. Cusp or Corner

6. Locate x values for each.
Vertical Tangent
Cusp or Corner
Discontinuity
Which points on the interval (-4,5) are continuous but not differentiable?

7. Can you locate any horizontal tangents
Can you locate any horizontal tangents? What does the derivative equal at a horizontal Tangent? Estimate the following: f’(-1)= f’(0)= f’(-2)=

8. Find the equation of the line that is tangent to each function
Find the equation of the line that is tangent to each function. (point slope form)
𝑓 5 =3 𝑓 ′ 4 =−2
𝑔(−1)=8 𝑔 ′ −1 =9
ℎ 5 =3 ℎ ′ 4 =−2

9. Homework Page 2

10. Name as many terms/notation that mean the same as (or are associated with) “derivative” as you can.
Here are a few: Instantaneous Rate of Change Slope Tangent Slope of a tangent line f’(x) dy/dx y’ Velocity or speed Quizlet: cards/

11. What is the difference between:
The equation of the line tangent to f(x) and the slope of the tangent line to f(x)
The Average Rate of Change and the Instantaneous Rate of Change
f(2)=3 and f’(2)=3
The slope of the secant and the slope of the tangent
Horizontal tangent and Vertical tangent

12. Quiz on Wednesday: Average rate of change/slope of a secant line.
“Find the derivative using the definition of derivative.” Yes, it will be on the quiz. I will choose one very similar to those in the video on my blog. The video shows step by step solutions to each.
Find an estimated derivative from a graph.
Identify points where function is or is not differentiable.
Vocab