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

Feb 24, 2017

Explanation:

The intermediate value theorem states that if

a continuous function $f \left(x\right)$, takes values $f \left(a\right)$ and $f \left(b\right)$,

within an interval $\left[a , b\right]$,

then it also takes any value between $f \left(a\right)$ and $f \left(b\right)$

at some point within the interval.

As such, if in case of a continuous function within a domain $\left[{x}_{1} , {x}_{2}\right]$,

if we identify two values in domain $\left[{x}_{1} , {x}_{2}\right]$, say $a$ and $b$, at which $f \left(x\right)$ takes opposite signs

then $f \left(x\right)$ must have a value $0$ i.e. a root, between $a$ and $b$ .