How do we use intermediate value theorem to identify zeros of a function?

1 Answer
Feb 24, 2017

Please see below.

Explanation:

The intermediate value theorem states that if

a continuous function #f(x)#, takes values #f(a)# and #f(b)#,

within an interval #[a, b]#,

then it also takes any value between #f(a)# and #f(b)#

at some point within the interval.

As such, if in case of a continuous function within a domain #[x_1,x_2]#,

if we identify two values in domain #[x_1,x_2]#, say #a# and #b#, at which #f(x)# takes opposite signs

then #f(x)# must have a value #0# i.e. a root, between #a# and #b# .