3.1 Power Rule
NOTES
Notation
Write your
questions here!
POWER RULE
Find the derivative of the following.
Rewrite and then take the derivative.
√
√
√
Evaluate
√
Find
|
Find
Higher Order Derivatives
√
Find Derivative on the Calculator
√
( )
Derivative means…
Slope at a point
Given
the slope at
Slope of the tangent line
find
Write the equation of the line
tangent to
at
Instantaneous rate of
change
What is the instantaneous rate
of change at 3 seconds?
Normal Line
Write the equation of the normal line at
and then graph it!
Derivative Rules
SUMMARY:
Constant Rule
Constant Multiple Rule
Power Rule
Sum/Difference Rule
(
)
PRACTICE
3.1 Power Rule
Find the derivative of the following.
1.
2.
3.
4.
5.
6.
7.
10.
√
√
√
√
13.
8.
√
√
9.
11.
12.
14.
15.
Find the derivatives of the following.
16.
17.
√
18.
√
Given
,
, and
19.
√ , find the following.
20.
22. Find the slope of
at
.
21.
23. At what value of x is
24. What is the slope of the tangent
line of
at the point (16, 4) ?
?
Find the slope of the tangent line.
25.
√
26.
27.
Is the slope of the tangent line positive, negative, or zero at the given point?
28.
at
29.
at
30.
Write the equation of the tangent line and the normal line at the point given.
31.
√
at
32.
at
√
at
The function is graphed below. Write the equation of the tangent line at the given point and graph it.
33.
at
34.
at
The function is graphed below. Write the equation of the normal line at the given point and graph it.
35.
at
36.
at
You will need to use a graphing calculator for 37-42
Use the graph to find the derivative of the function at the given value. Round to nearest thousandth.
37.
38.
at
at
39.
at
Write the equation of the tangent line at the point given and sketch the graph. Round to nearest thousandth.
40.
√
at
41.
at
42.
at
TEST PREP
3.1 Power Rule
MULTIPLE CHOICE
1. Let
. What is the x-coordinate of a point where the instantaneous rate of change of f is the
same as the average rate of change of f on the interval
?
(A)
√
(B)
(C)
(D)
(E) √
2. Given
where b is a constant, find the value of b if
.
(A)
(B)
(C)
(D)
(E) none of the above
3. Given
where
and
, write an equation for the line which is tangent to the graph of
at the point
.
(A)
(B)
(C)
(D)
(E)
4. If the line normal to the graph of
gives the value of
(A)
(B)
(C)
(D)
(E)
at the point
passes through the point
, then which of the following
You are allowed to use a graphing calculator for #5
5. Which of the following is an equation of the line tangent to the graph of
?
(A)
at the point where
(B)
(C)
(D)
(E)
FREE RESPONSE
Your score: ____ out of 5
Use the table to answer the questions below.
0
2
5
-10
-4
20
1
5
11
2
2
2
-7
-1
83
3
7
58
-4
8
26
1. Find the average rate of change of f over the interval
. Find the value of x at which the
instantaneous velocity of g is equal to the average rate of change of f over the interval
.
2. Write the equation of the line normal to
3.
4.
at the point where
.