Mathematics · essential
Second 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
\[f'(a)=0,\ f''(a)>0\Rightarrow f(a)\text{ local minimum};\qquad f'(a)=0,\ f''(a)<0\Rightarrow f(a)\text{ local maximum}\]
Variables: \(a\) is a critical point.
Conditions: If \(f''(a)=0\), test is inconclusive.
Quick maxima-minima classification.