Calculus

Intermediate Value Theorem (IVT) If a function $f(x)$ is continuous on a closed interval $[a, b]$ and $k$ is any number between $f(a)$ and $f(b)$, then there is at least one number $c$ in the interval $[a, b]$ such that $f( c) = k$. The intermediate value theorem has two conditions: Function $f$ is continuous over the interval $[a, b]$. The value $d$ lies between $f(a)$ and $f(b)$ We must establish these two conditions to conclude that there is a value $c$ in the interval $[a, b]$ for which $g(x) = d$ (another way to phrase this conclusion is that the equation $g(x) = d$ has a solution where $a <= x <= b$)....