Agenda.

1

• Agenda.
• Check answers to HW from weekend. I also posted
  answers on line.
• Check answers to last nights homework on
  continuity.
• Complete review worksheets. Answers are posted
  online and a few copies are with the substitutes
  for you to check.
• Quiz on limits, continuity and derivatives on
  Thursday. We will go over the quiz and these
  worksheets on Wednesday in class.
• My expectation is you work the whole period
  efficiently, checking your answers with the keys
  provided and discussing the questions with your
  peers as needed.

2
1. Given k(x) find a and b so the function is
continuous.
3
2. Given j(x) find a and b so the function is
continuous.
4
3. Given w(x) find a and b so the function is
continuous.
5
Review Worksheet
6

• Given f(x), is f(x) continuous at x -4?

7
2. Given g(x), is g(x) continuous at x 2?
8

1. Given f(x) -3x2 8x 5, find the slope of the
   tangent line when x approaches 3 using the
   definition.

9
4. Given f(x) -3x2 8x 5, what is the
equation of the tangent line as x approaches 3?
10
5. Given f(x) -3x2 8x 5, find the
derivative function of f(x) using the definition.
11
6. What is the slope of the tangent line using
your result from 5 as x approaches 3?
7. Does your answer in 6 match your answer in
3?
12

1. Using the graph below, for what values of x is
   the derivative positive, negative, and zero?
   Assume integer values for x.

13
9. Using the graph below, for what values of x
is the derivative positive, negative, and zero?
Assume integer values for x.
14
Use the graph of f(x) below for problems 10 13.

15
10. The graph below is f(x), for what values of x
is the function not continuous?
11. The graph below is f(x), for what values of x
does the limit not exist?
16
12. The graph below is f(x), for what values of x
does the derivative not exist?
13. Draw f'(x) on the grid.
17
14. Use the graph of f'(x) below to draw
f(x). NOTE This is the derivative function.
18
15. Find the derivative of
19
16. Find the derivative of
20
17. Find the derivative of f(x) 1/(x 4).
21
18. Find the derivative of j(x) sin(x).
22
Review Worksheet Answers
23

• Given f(x), is f(x) continuous at x -4?

24
2. Given g(x), is g(x) continuous at x 2?
25

1. Given f(x) -3x2 8x 5, find the slope of the
   tangent line when x approaches 3 using the
   definition.

26
4. Given f(x) -3x2 8x 5, what is the
equation of the tangent line as x approaches 3?
27
5. Given f(x) -3x2 8x 5, find the
derivative function of f(x) using the definition.
28
6. What is the slope of the tangent line using
your result from 5 as x approaches 3?
7. Does your answer in 6 match your answer in
3?
29
7. Does your answer in 6 match your answer in
3?
30

1. Using the graph below, for what values of x is
   the derivative positive, negative, and zero?
   Assume integer values for x.

31
9. Using the graph below, for what values of x
is the derivative positive, negative, and zero?
Assume integer values for x.
32
Use the graph of f(x) below for problems 10 13.

33
10. The graph below is f(x), for what values of x
is the function not continuous?
11. The graph below is f(x), for what values of x
does the limit not exist?
34
12. The graph below is f(x), for what values of x
does the derivative not exist?
13. Draw f'(x) on the grid.
35
14. Use the graph of f'(x) below to draw
f(x). NOTE This is the derivative function.
36
15. Find the derivative of
37
16. Find the derivative of
38
17. Find the derivative of f(x) 1/(x 4).
39
18. Find the derivative of j(x) sin(x).