함수의 증가, 감소

Definition

Definition. Let $x_1, x_2 \in$ an interval $I$ such that $x_1 < x_2$ and let $f: I \longrightarrow \mathbb{R}$.
We say $f$ is increasing on $I$ if $$f(x_1) < f(x_2) $$ and $f$ is decreasing on $I$ if $$f(x_1) > f(x_2). $$

Theorem

Theorem. Let $f: I \longrightarrow \mathbb{R}$ be a differentiable function on $I$. Then for $\forall x \in I$,
$$f'(x) > 0 \Longrightarrow f \text{ is increasing on } I$$ and $$f'(x) < 0 \Longrightarrow f \text{ is decreasing on } I.$$

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References are here: 

(1) http://www.yes24.com/Product/Goods/97032834

Calculus, 9/E (Metric Version : Early Transcendentals) - 예스24