335
Answers
501–600
Answers and Explanations
Keeping the positive solution (either works), you have y =
=
3
2
3 2
2
, which gives you
the following x value:
x =
−
=
−
=
−
=
4 4
9
3 2
2
4 4
9
9 2
4
4 2
2
2

 

 

 

 
( )
Therefore, the area of the rectangle is
A =
=
4 2 3 2
2
12

 

 
Note that you can verify that the value y =
=
3
2
3 2
2
does indeed give a maximum by
using the first derivative test.
513.
0.84771
Use the formula x
x
f x
f x
n
n
n
n
+
( )
( )
1 =
− ’
with f
 
(x) = x
3
+ 4x – 4, f
 
'(x) = 3x
2
+ 4, and x 1 = 1. Note
that the formula gives you x
x
f x
f x
2
1
1
1
= −
( )
( )
’
, x
x
f x
f x
3
2
2
2
= −
( )
( )
’
, and so on. Therefore,
you have
x
x
2
3
2
3
3
2
1
1
4 1 4
3 1
4
6
7
6
7
6
7
4 6
7
4
3 6
7
4
451
5
= −
+
−
+
=
= −
+
−
+
=
( )
( )
( )
( ) ( )
( )
3 32
0 84774
0 84774
0 84774
4 0 84774 4
3 0 84774
4
4
3
2
≈
=
−
+
−
+
.
.
( .
)
( .
)
( .
)
x
≈ ≈
=
−
+
−
+
≈
0 84771
0 84771
0 84771
4 0 84771 4
3 0 84771
4
0
5
3
2
.
.
( .
)
( .
)
( .
)
x
. .84771
514.
2.0597671
Use the formula x
x
f x
f x
n
n
n
n
+
( )
( )
1 =
− ’
with f
 
(x) = x
4
– 18, f
 
'(x) = 4x
3
, and x 1 = 2. Note that
the formula gives you x
x
f x
f x
2
1
1
1
= −
( )
( )
’
, x
x
f x
f x
3
2
2
2
= −
( )
( )
’
, and so on. Therefore, you have