Calculus AB Mrs. Hill
Here are the classwork examples that were done on 11/27/07.
Please email me if you have any questions.
Use the table on page 147 (#57) to answer the following questions.
at x = 1
at x = 0
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
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 =
Integrate each of the following:
2. 9sin(43 x) dx =
3x 2 4 x + 5
6. sin 2 (16 x)dx
5e6 x 81
Hint just sin
Hint long Divide
7. sec 2 4 xdx =
8. tan 2 2 xdx =
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
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
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 =
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 +
A function f(x) is continuous at x = c if the following three conditions are met:
f(c) is defined.
A function is continuous on an open interval (a, b) if it is continuous at each point in the
If f(x) is
Chain rule worksheet.
Show all work on a separate sheet of paper. No calculator.
1. Find the derivative of the functions.
2. Determine the points on the interval at which the graph of has a horizontal tangent.
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,
its distance is given by s =
feet from its initial p