Home/Differential Calculus/Critical points and extrema/Formula8.3. Critical points and extremaFormulaIn 8.3. Critical points and extremaFormulaCopy LaTeXf′(x) changes from − to + on c⇒f local minimum at cf'(x)\text{ changes from }-\text{ to }+\text{ on }c \Rightarrow f\text{ local minimum at }cf′(x) changes from − to + on c⇒f local minimum at cTagsAnalysisCritical points and extremaDifferential calculusDerivativeVariablesxxxIndependent variableaaaPoint or real constantcccIntermediate point (MVT, Rolle)fffFunctionf′f'f′Derivative of fffRelated topicsOptimizationFound an error? Contact us.Related formulasRelatedFormulaf′(x) changes from + to − on c⇒f local maximum at cf'(x)\text{ changes from }+\text{ to }-\text{ on }c \Rightarrow f\text{ local maximum at }cf′(x) changes from + to − on c⇒f local maximum at cOpen formulaOpen in sectionRelatedFormulaf′(c)=0, f′′(c)<0⇒f has a local maximum at cf'(c)=0,\ f''(c)<0 \Rightarrow f\text{ has a local maximum at }cf′(c)=0, f′′(c)<0⇒f has a local maximum at cOpen formulaOpen in sectionRelatedFormulaf′(c)=0, f′′(c)>0⇒f has a local minimum at cf'(c)=0,\ f''(c)>0 \Rightarrow f\text{ has a local minimum at }cf′(c)=0, f′′(c)>0⇒f has a local minimum at cOpen formulaOpen in sectionRelatedFormulaf′(c)=0 or f′(c) does not exist⇒c is a critical pointf'(c)=0\ \text{or}\ f'(c)\text{ does not exist} \Rightarrow c\text{ is a critical point}f′(c)=0 or f′(c) does not exist⇒c is a critical pointOpen formulaOpen in section