Resposta
If $f'(c) = 0$ and $f''(c) > 0$, $f(c)$ is a local minimum; if $f'(c) = 0$ and $f''(c) < 0$, $f(c)$ is a local maximum.
Explicação
If $f''(c) = 0$, the test is inconclusive and higher derivatives or sign changes of $f'(x)$ must be examined.
Início / Biblioteca / JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry / Flashcard sintético
What is the condition for an extremum (local minimum or maximum) of a function $f(x)$ using second derivatives?
Flashcard de estudo do deck JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry.