Question

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

Answer 1

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` .