41
Chapter 3: Limits and Rates of Change
270. By checking only the endpoints of each
interval, determine which interval
contains a solution to the equation
2(3
x
) + x
2
– 4 = 32 according to the
intermediate value theorem:
(A) [0, 1]
(B) [1, 2]
(C) [2, 3]
(D) [3, 4]
(E) [4, 5]
271. By checking only the endpoints of each
interval, determine which interval contains a solution to the equation
4 2
3 5 22
x − + =
according to the
intermediate value theorem:
(A) [0, 1]
(B) [1, 2]
(C) [2, 3]
(D) [3, 4]
(E) [4, 5]
The Intermediate Value
Theorem
268–271 Determine which of the given intervals is
guaranteed to contain a root of the function by the
intermediate value theorem.
268. By checking only the endpoints of each
interval, determine which interval contains a root of the function f x
x
( ) =
−
2
3
2
by the intermediate value theorem:
(A) [–5, –4]
(B) [–4, –3]
(C) [0, 1]
(D) [1, 2]
(E) [5, 12]
269. By checking only the endpoints of each
interval, determine which interval
contains a root of the function
f x
x
x
( ) =
−
+
3
4
5 by the intermediate
value theorem:
(A) [0, 1]
(B) [1, 4]
(C) [4, 9]
(D) [9, 16]
(E) [16, 25]