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Application of Differentiation

최댓값과 최솟값(Maximum and Minimum Values) : http://me2.do/xt1c7qD7

극값정리(The Extreme Value Theorem) : http://me2.do/GE2p3z4H

Fermat's Theorem

Rolle's Theorem

The Mean Value Theorem

$f'(x)=0 \text{ on } (a,b) \Rightarrow f(x)=c \text{ on } (a,b)$

$f'(x)=g'(x) \text{ on } (a,b) \Rightarrow f(x)=g(x)+c \text{ on } (a,b)$

Increasing/Decreasing Test

The First Derivative Test

concave upward and concave downward

오목 검사(Concavity Test) : http://me2.do/5oFSwRYk

inflection point

The Second Derivative Test

$\displaystyle\lim_{x\rightarrow \infty} f(x) = L : \forall \varepsilon , \exists N \  s.t. \  x>N \Rightarrow |f(x)-L|<\varepsilon $

$\displaystyle\lim_{x\rightarrow -\infty} f(x) = L : \forall \varepsilon , \exists N \  s.t. \  x<N \Rightarrow |f(x)-L|<\varepsilon $

$\displaystyle\lim_{x\rightarrow \infty} f(x) = \infty : \forall M , \exists N \  s.t. \  x>N \Rightarrow f(x)>M $

$\displaystyle\lim_{x\rightarrow -\infty} f(x) = \infty : \forall M , \exists N \  s.t. \  x<N \Rightarrow f(x)>M $