Answers and Explanations 237
Answers
301–400
Setting each factor equal to zero gives you 3x + 1 = 0, which has the solution x = − 1
3
,
and gives you x – 1 = 0, which has the solution x = 1.
311.
± 1
3 2
Begin by finding the derivative of the function:
f x
x
' ( ) =
+
18
5
2
Next, set the derivative equal to 6 and solve for x:
18
5 6
1
18
1
18
1
3 2
2
2
x
x
x
x
+ =
=
= ±
= ±
312.
16x
7
+ 5x
4
– 8x
3
– 1
Recall that the product rule states
d
dx
f x g x
f x g x f x g x
( ) ( )
 
  = ( ) ( )+ ( ) ( )
'
'
You can multiply out the expression f
 
(x) = (2x
3
+ 1)(x
5
– 1) first and then avoid using
the product rule, but here’s how to find the derivative using the product rule:
f x
x
x
x
x
x
x
x
x
x
x
' ( ) = ( ) −
(
) + +
(
) −
(
)
=
−
+
−
+
−
=
6
2
1 5
1
6
6
10
2
5
1
16
2
5
3
4
7
3
7
3
4
x x
x
x
7
4
3
5
8
1
+
−
−