Mathematics · essential
First derivative test for local extrema for JEE
Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
Formula
\[\begin{aligned}f'\text{ changes }+\to -&\Rightarrow \text{local maximum},\\ f'\text{ changes }-\to +&\Rightarrow \text{local minimum},\\ \text{no sign change}&\Rightarrow \text{no extremum at that critical point}\end{aligned}\]
Variables: Signs are checked around a critical point.
Conditions: Requires sign analysis of \(f'\) in neighborhoods.
Local maxima-minima problems.