# Suppose f is a function defined on [a,b]. Let N be a number with f(a) < N < f(b). Then there...

## Question:

Suppose f is a function defined on {eq}[a,b]{/eq}. Let N be a number with f(a) < N < f(b). Then there exists c in (a, b) such that f(c) = N. Why is this statement false?

## Intermediate value theorem

Let f(x) is a continuous function defined on {eq}[a,b]{/eq}. Let m be a number with f(a) < m < f(b). Then there exists c in (a, b) such that f(c) = m. Every continuous function attained all the values in between f(a) and f(b).