Existence and Uniqueness of a Solution

Existence and Uniqueness of a Solution

If $$f(x)$$ is continuous on $$[a,b]$$, strictly monotonic on $$[a,b]$$, and:

$$k\in[f(a),f(b)]$$

then:

$$f(x)=k$$

has exactly one solution in $$[a,b]$$.

Usage

- Used to prove that an equation has exactly one solution in a specified interval.