CALCULUS BC
WORKSHEET ON INTERMEDIATE VALUE THEOREM
Work the following on notebook paper.
On problems 1 – 4:
(a) Determine if the Intermediate Value Theorem holds for the given value of
k
. (b) If
the theorem holds, find a number
c
for which
f c k
( )
=
.
If the theorem does
not
hold,
give the reason.
(c) Draw a sketch of the curve and the line
y k
=
.
1 1
[ ] 0 2
1.
( ) [ ]
f x a b k
= = =
+
, , , ,
1 5
x
1 3
[ ] 0 2
2.
( ) [ ]
f x a b k
= = =
+
, , , ,
1 4
x
3.
( ) [ ]
2
f x x x a b k
= − − = − = −
3 4 [ ] 2 3 2
, , , ,
2
4.
( ) [ ] [ ]
f x x a b k
= − = − =
9 , , 3, 1 , 2
______________________________________________________________________________
5. Given the function
( )
2
f x x x
= + −
2 5.
(a) Does
f x
( )
=
7somewhere on the interval
[
−
1, 3
]
? Use the Intermediate Value Theorem to
show why or why not.
(b) Does
f x
( )
=
12somewhere on the interval
[
−
1, 3
]
? Use the Intermediate Value Theorem to
show why or why not.
6. Use the Intermediate Value Theorem to show that
3
x x
+ =
0has a root in the interval
[
−
1, 2