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chapter 2 section 4.notebook February 15, 2017 (1, 6) and (4, -1)

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Page 1: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

(1, 6) and (4, -1)

Page 2: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 3: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 4: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 5: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 6: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 7: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Graphically displaying the slope for a tangent line at a point on a curve.

Page 8: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 9: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

STOPdate ____

Example:  Find the slope of the tangent line to the function at x = 1.f(x) = 4 - x2

STOPdate ____

Page 10: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Example: a. Find the slope of the tangent line to the function at x = 2.b. Find the slope of a tangent line at the value x = a.

f(x) = 1x

Example:  Find the slope of the tangent line to the function at x = 3.

f(x) = x3 + 1

Page 11: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Find the values of x on the function y = 2x2 - 8x that have horizontal tangents.

When do you think a function would not have a Tangent line at a given point???

2 - 2x - x2 , x < 0f(x) =

2x - 2 , x > 0

at points of discontinuity and at point where there are corners and cusps...ask why!?

{

Page 12: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 13: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 14: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 15: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 16: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 17: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

Page 18: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017

35. will exist as a perpendicular to the tan line36. no...right and left hand limits not same37. D38. E39. C40. A

Page 19: chapter 2 section 4.notebook - Hendrick Hudson Central ... · chapter 2 section 4.notebook February 15, 2017 Example: a. Find the slope of the tangent line to the function at x =

chapter 2 section 4.notebook February 15, 2017