Definition
- We say that \(f\) is increasing on \((a,b)\) if for all \(a < x_1 < x_2 < b\), $$f(x_1) \leq f(x_2).$$
- We say that f is strictly increasing on \((a,b)\) if for all \(a < x_1 < x_2 < b\), $$f(x_1) < f(x_2).$$
- We say that f is decreasing on \((a,b)\) if for all \(a < x_1 < x_2 < b\), $$f(x_1) \geq f(x_2).$$
- We say that f is strictly decreasing on \((a,b)\) if for all \(a < x_1 < x_2 < b\), $$f(x_1) >f(x_2).$$
References
- Introduction to Analysis, An, 4th edition by William Wade
- Lecture Notes by Professor Chun Kit Lai