Ada

홈 / 라이브러리 / Gaokao essentials: original practice / AI 플래시카드

For a differentiable function $f(x)$, how does the first derivative test determine a local extremum at critical point $x_0$ ($f'(x_0) = 0$)?

덱 'Gaokao essentials: original practice'의 플래시카드.

정답

If $f'(x)$ changes from positive to negative at $x_0$, $f(x_0)$ is a local maximum; if from negative to positive, a local minimum.

해설

If $f'(x)$ does not change sign around $x_0$, $x_0$ is an inflection point or saddle rather than a local extremum.

AI 생성 콘텐츠 · 감수: Ada