What does “Critical points” actually mean in Application of Derivatives, and why does it matter for JEE?
a point of a function where f′(x)=0 or f′(x) is undefined (including possible endpoints).
In simple words: a critical point of a function is any point where the derivative vanishes or fails to exist (for example at cusps, corners or endpoints). Such points are candidates for maxima, minima or points of inflection, and JEE problems often ask you to identify and test them.
Key point
Critical points
Common mistake
thinking every point where f'(x)=0 is a maximum.
Memory tip
f'(x)=0 finds candidates; a further test says max, min or neither.
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