Answer:
For problems 1 – 12 find the derivative of the given function.
f
(
x
)
=
6
x
3
−
9
x
+
4
Solution
y
=
2
t
4
−
10
t
2
+
13
t
Solution
g
(
z
)
=
4
z
7
−
3
z
−
7
+
9
z
Solution
h
(
y
)
=
y
−
4
−
9
y
−
3
+
8
y
−
2
+
12
Solution
y
=
√
x
+
8
3
√
x
−
2
4
√
x
Solution
f
(
x
)
=
10
5
√
x
3
−
√
x
7
+
6
3
√
x
8
−
3
Solution
f
(
t
)
=
4
t
−
1
6
t
3
+
8
t
5
Solution
R
(
z
)
=
6
√
z
3
+
1
8
z
4
−
1
3
z
10
Solution
z
=
x
(
3
x
2
−
9
)
Solution
g
(
y
)
=
(
y
−
4
)
(
2
y
+
y
2
)
Solution
h
(
x
)
=
4
x
3
−
7
x
+
8
x
Solution
f
(
y
)
=
y
5
−
5
y
3
+
2
y
y
3
Solution
Determine where, if anywhere, the function
f
(
x
)
=
x
3
+
9
x
2
−
48
x
+
2
is not changing. Solution
Determine where, if anywhere, the function
y
=
2
z
4
−
z
3
−
3
z
2
is not changing. Solution
Find the tangent line to
g
(
x
)
=
16
x
−
4
√
x
at
x
=
4
. Solution
Find the tangent line to
f
(
x
)
=
7
x
4
+
8
x
−
6
+
2
x
at
x
=
−
1
. Solution
The position of an object at any time t is given by
s
(
t
)
=
3
t
4
−
40
t
3
+
126
t
2
−
9
.
Determine the velocity of the object at any time t.
Does the object ever stop changing?
When is the object moving to the right and when is the object moving to the left?
Solution
Determine where the function
h
(
z
)
=
6
+
40
z
3
−
5
z
4
−
4
z
5
is increasing and decreasing. Solution
Determine where the function
R
(
x
)
=
(
x
+
1
)
(
x
−
2
)
2
is increasing and decreasing. Solution
Determine where, if anywhere, the tangent line to
f
(
x
)
=
x
3
−
5
x
2
+
x
is parallel to the line
y
=
4
x
+
23
. Solution
