Part II: The Answers
236
Answers
301–400
Next, apply the power rule to find the derivative:
f x
x
x
x
x
' ( ) = −
−
−
= −
−
−
−
−
1
2
2
1
2 2
2
3
2
3
307.
−
+
−
5
2 20
6
3
x
x
Begin by multiplying the factors together:
f x
x
x
x
x
x
x
x
x
x
x
( ) =
+
(
) −
(
)
=
−
+
−
=
−
−
−
−
−
−
−
−
−
3
2
5
2
2
5
2
4
5
5
4
20
20
Then find the derivative using the power rule:
f x
x
x
x
x
' ( ) = −
+
−
= −
+
−
−
−
5
2
20
5
2 20
6
3
6
3
308.
16x
3
– 2x + 8
Apply the power rule to each term, recalling that the derivative of a constant is zero:
f ' (x) = 16x
3
– 2x + 8.
309.
1
2
1
4
1 2
5 4
x
x
+
Rewrite the function using exponential notation:
f x
x
x
x
x
x
x
( ) =
−
=
−
=
−
−
1
1
4
1 2
1 4
1 2
1 4
Then apply the power rule to each term to find the derivative:
f x
x
x
x
x
' ( ) =
− −
(
)
=
+
−
−
1
2
1
4
1
2
1
4
1 2
5 4
1 2
5 4
310.
− 1
3
, 1
Begin by finding the derivative of the function f
 
(x) = x
3
– x
2
– x + 1:
f x
x
x
' ( ) =
−
−
3
2 1
2
A horizontal tangent line has a slope of zero, so set the derivative equal to zero, factor,
and solve for x:
3
2
1 0
3
1
1 0
2
x
x
x
x
−
− =
+
(
) −
(
)=