Increasing and Decreasing Intervals of a Function - Expii

We discuss the calculus of monotonic functions (especially in terms of derivatives). A differentiable function f is weakly increasing (resp. weakly decreasing) on (a,b) if and only if the derivative function f' is non-negative (resp. non-positive) on (a,b). A differentiable function f is strictly increasing (resp. strictly decreasing) on (a,b) if and only if f' is non-negative (resp. non-positive) on (a,b) and every interior stationary point c in (a,b) of f is a saddle point.