What does “Second-derivative test” actually mean in Application of Derivatives, and why does it matter for JEE?
at a critical point, f''>0 means a local minimum (cup up) and f''<0 means a local maximum (cap down).
In simple words: at a critical point, f''>0 means a local minimum (cup up) and f''<0 means a local maximum (cap down). Getting Second-derivative test clear matters because JEE questions on Application of Derivatives usually test this idea directly, not just a formula you memorised.
Key point
Second-derivative test
Common mistake
confusing which sign of f'' gives a maximum.
Memory tip
f'' positive = valley (min); f'' negative = hill (max).
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