Homework/Test Review from 3/13...Homework/Test Review from 3/13 3-14 Definition of a...
Transcript of Homework/Test Review from 3/13...Homework/Test Review from 3/13 3-14 Definition of a...
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
.