Calculus AB Mrs. Hill
Here are the classwork examples that were done on 11/27/07.
Please email me if you have any questions.
Find .
1.
2.
3.
Use the table on page 147 (#57) to answer the following questions.
4.
at x = 1
5.
at x = 0
Answers:
1.
2.
3.
4. -3
Average Rate of Change = Slope of a Secant Line = Average Velocity
Given f(x) and [a, b]:
Avg. roc =
Instantaneous Rate of Change = Slope of a Tangent Line = Instantaneous
Velocity
Given f(x) and x = a:
Ins. roc =
Example 1: Find the average rate of chang
Calculus AB AP
Final Review # 1
1. 3e 4 x dx =
Name
Integrate each of the following:
2. 9sin(43 x) dx =
3.
3x
dx =
5x2 7
4.
5.
3x 2 4 x + 5
dx =
x+3
6. sin 2 (16 x)dx
2e6 x
dx =
5e6 x 81
Hint just sin
Hint long Divide
7. sec 2 4 xdx =
8. tan 2 2 xdx =
Hin
The Extreme Value Theorem
If f(x) is continuous on a closed interval [a, b], then f(x) has both a maximum value and a
minimum value.
Steps:
1. Find f (x).
2. Find the values of x where f (x) = 0 or undefined.
3. Substitute the x values found in step 2 tha
Calculus AB AP
Final Review # 2
Name
Find the derivative of each of the following:
1. y = 3 x 2 5 x + 9
2. y = 5sin 4 (9 x)
3. y = ln(7 x 3)
5. y =
3x 2
6 9x
4. y = 4 x (3 x 7)3
6. y = tan 6 x + cot 4 x 9e 2 x
7. y = ecos(4 x )
8. y = 4sec6 (7 x)
9. y 2 +
2.3: Continuity
A function f(x) is continuous at x = c if the following three conditions are met:
1.
2.
3.
f(c) is defined.
exists.
= f(c)
A function is continuous on an open interval (a, b) if it is continuous at each point in the
interval.
If f(x) is
Name:_
Date:_
Chain rule worksheet.
Show all work on a separate sheet of paper. No calculator.
1. Find the derivative of the functions.
a.
b.
c.
d.
e.
f.
g.
h.
i.
2. Determine the points on the interval at which the graph of has a horizontal tangent.
3.
4
Calculus AB
Name:_
Position Function Review
Solve each problem, label units when necessary and SHOW ALL WORK.
1. A particle moves in a straight line from its initial position so that after t seconds,
5t
its distance is given by s =
feet from its initial p