Part II: The Answers
312
Answers
401–500
482.
− 16
3
Notice that the given function is differentiable on (–8, 0). Then verify that f (–8) = f
(0)
so that Rolle’s theorem can be applied:
f
f
−
( )= − − + = −
=
( ) =
+ =
8
8
8 8
8 0 0
0 0 0 8 0
Next, find the derivative of the function, set it equal to zero, and solve. Here’s the
derivative:
′
(
)
f c
c
c
c
c
c
c
c
( ) (
)
(
)
(
)
=
+
+
+
= ( + )
+ +
=
+
−
−
1
8
1
2
8
8
8 1
2
3
2
8
1 2
1 2
1 2
c c + 8
Setting the numerator equal to zero and solving for c gives you
3
2
8 0
3
2
8
16
3
c
c
c
+ =
= −
= −
312
Answers
401–500
482.
− 16
3
Notice that the given function is differentiable on (–8, 0). Then verify that f (–8) = f
(0)
so that Rolle’s theorem can be applied:
f
f
−
( )= − − + = −
=
( ) =
+ =
8
8
8 8
8 0 0
0 0 0 8 0
Next, find the derivative of the function, set it equal to zero, and solve. Here’s the
derivative:
′
(
)
f c
c
c
c
c
c
c
c
( ) (
)
(
)
(
)
=
+
+
+
= ( + )
+ +
=
+
−
−
1
8
1
2
8
8
8 1
2
3
2
8
1 2
1 2
1 2
c c + 8
Setting the numerator equal to zero and solving for c gives you
3
2
8 0
3
2
8
16
3
c
c
c
+ =
= −
= −