미분의 응용(Application of Differentiation)

• 최댓값과 최솟값(Maximum and Minimum Values)

  [PDF] [영상(YouTube)]

• 극값정리(The Extreme Value Theorem)

  [PDF] [영상(YouTube)]

• 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)

  [PDF] [영상(YouTube)] [Geogebra Tube]

• 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 $