Mathematics · important
Non-decreasing and non-increasing criteria for JEE
Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
Formula
\[f'(x)\ge 0\Rightarrow f\text{ non-decreasing},\qquad f'(x)\le 0\Rightarrow f\text{ non-increasing}\]
Conditions: On an interval where derivative exists and satisfies the inequality.
Theoretical monotonicity questions.