Home/Differential Calculus/Concavity/Formula8.2. ConcavityFormulaIn 8.2. ConcavityFormulaCopy LaTeXf′′(x)<0 on I⇒f concave down on If''(x)<0\text{ on }I \Rightarrow f\text{ concave down on }If′′(x)<0 on I⇒f concave down on ITagsAnalysisConcavityDifferential calculusDerivativeVariablesxxxIndependent variablecccIntermediate point (MVT, Rolle)fffFunctionf′f'f′Derivative of ffff′′f''f′′Second derivative of fffFound an error? Contact us.Related formulasRelatedFormulaf′′(x)>0 on I⇒f concave up on If''(x)>0\text{ on }I \Rightarrow f\text{ concave up on }If′′(x)>0 on I⇒f concave up on IOpen 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