Download presentation

Presentation is loading. Please wait.

Published byLuis Rhodes Modified over 3 years ago

1
2.9 Derivative as a Function

2
From yesterday: the definition of a derivative: The derivative of a function f at a number a, denoted by is: if this limit exists Another useful form of the derivative occurs if we write x = a + h, then h = x – a, and h approaches zero as x approaches a

3
A function f is differentiable at a if f(a) exists. It is differentiable on an open interval (a,b) IF it is differentiable at EVERY NUMBER in the interval. Theorem: If f is differentiable at a, then f is continuous at a. The converse of this theorem is false. There are many functions that are continuous but not differentiable.

4
If, find a formula for & graph it on the next page

5

6
If find the derivative of f. State the domain of f

7
Given, graph its derivative:

8
Other notations for the derivative: A function f is differentiable at a if fa exists. It is differentiable on an open interval or IF it is differentiable at EVERY number in the interval.

9
When is differentiable????

10
If f is differentiable at a, then f is continuous at a. Why???

11

12

13
Read p. 165 – 173 Work p. 173 # 1, 5, 14, 21, 22, 23, 33, 37, 44

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google