1. 3.2. Definition of Derivative.
Differentiability on the closed interval and at the point.
Corners, cusps, vertical tangent.
Domain of the derivative.
Rita Korsunsky

2. Definition of Derivative

3. Example 1

4. Example 2

5. Applications of Derivative
Notations of Derivative
Why quotient ? Next slide…
Not common
Higher derivatives

7. Example 3

8. Differentiability on a Closed Interval
A function f is differentiable on a closed interval [a,b] if f is differentiable on the open interval (a,b) and if the following limits exist:

9. Example 4

11. P(5,0)
P(-5,0) l1 l2
y = f(x)
P(a, f(a)) l y

12. Example 5 -5

13. Theorem Proof: f is continuous at a
If a function f is differentiable at a, then f is continuous at a.
Proof:
f is continuous at a