Question

The table below gives for the value of continuous function f at each x-value. Using the Intermediate Value Theorem and the information in the table, determine the smallest interval in which the function must have a root.


x f(x)

−5 −1.25

−4 −2.03

−3 −3.05

−2 3.01

−1 1.02

0 0.69

1 4.43

2 9.45

3 2.76

4 0.93

5 0.13

Answer (in interval notation):

Answer 1

According to the intermediate value theorem the interval (a,b) contains a root if this condition holds

$f(a)f(b)<0$

Since $f(-3)f(-2) < 0$ , hence (-3,-2) contains a root. Then

(-3,-2) is the smallest interval that contains a root