3-14 Definition of a Derivative.notebook March 14, 2014

Homework/Test Review from 3/13

3-14 Definition of a Derivative.notebook March 14, 2014

3-14 Definition of a Derivative.notebook March 14, 2014

By the end of this lesson, students will be able to:

1. Find the slope at a point.

2. Find an equation of the tangent line.

3. Examine the link between differentiability and

continuity.

4. Interpret differentiability graphically.

Change is Good

3-14 Definition of a Derivative.notebook March 14, 2014

https://www.khanacademy.org/math/calculus/differential-calculus/derivative_intro/

v/calculus--derivatives-1--new-hd-version

Let's Dig a Little Deeper

3-14 Definition of a Derivative.notebook March 14, 2014

Ex. 1) How would you evaluate the

derivative of f(x) = at (1,1)?

3-14 Definition of a Derivative.notebook March 14, 2014

Ex. 2) Find an equation of the tangent line to

at (2,4).

3-14 Definition of a Derivative.notebook March 14, 2014

The derivative of f at c is

provided the limit exists.

Alternate Form of the Derivative

* Use this form to determine if a function is

differentiable.*

3-14 Definition of a Derivative.notebook March 14, 2014

Differentiability and Continuity

What does it mean for a function to be

continuous?

What does it mean for a function to be

differentiable?

3-14 Definition of a Derivative.notebook March 14, 2014

Ex. 3) Is f(x) = | x - 2 | differentiable at x=2?

3-14 Definition of a Derivative.notebook March 14, 2014

Ex. 4) Is f(x)= differentiable at x=0?

3-14 Definition of a Derivative.notebook March 14, 2014

Relationship Status

If a function is differentiable at x = c, then it is

continuous at x = c.

If function is continuous at x = c, it is not

necessarily differentiable at x = c.

Sharp turn or vertical tangent = not differentiable.

3-14 Definition of a Derivative.notebook March 14, 2014

Homework

Page 99 Exercises 17-25 odd, 45-59 odd

3-14 Definition of a Derivative.notebook March 14, 2014

Think Critically

Find an equation of the line that is tangent to

the graph and parallel to the line

.