Monotonicity from sign of derivative (f' > 0 on interval ⇒ f strictly increasing; f' < 0 ⇒ strictly decreasing)

jee-mainjee-advanced

f' > 0 on interval ⇒ f strictly increasing; f' < 0 ⇒ strictly decreasing

What each symbol means

SymbolWhat it stands for
f'(x)Derivative on open interval I

When to use this

f continuous on I and differentiable on interior (standard JEE use). f'=0 at isolated points can still allow strict increase if f'≥0 and only discrete zeros.