The Intermediate Value Theorem - Practice Questions & MCQ

The Intermediate Value Theorem (IMVT)

Let $f$ be continuous over a closed interval $[a, b]$ and $f(a) \neq f(b)$. If $z$ is any real number between $f(a)$ and $f(b)$, then there is at least one $x$ in $[a, b]$ satisfying $f(x)=z$

An important result from IMVT

If $f(x)$ is a continuous function in $[a, b]$ and $f(a)$ and $f(b)$ are of opposite signs, then there is at least one root of $f(x)$ lying in $(a, b)$.