Mathematics · essential
Increasing and decreasing via first derivative for JEE
Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
Formula
\[f'(x)>0\Rightarrow f\text{ increasing},\qquad f'(x)<0\Rightarrow f\text{ decreasing}\]
Conditions: On an interval where derivative sign is maintained.
Monotonicity and interval analysis.