Home/Differential Calculus/Concavity/Formula8.2. ConcavityFormulaIn 8.2. ConcavityFormulaCopy LaTeXf′′(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 ITagsAnalysisConcavityDifferential calculusDerivativeExplore the ideaExplore the ideaVariablesxxxIndependent 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 (a,b)⇒f decreasing on [a,b]f'(x)<0\text{ on }(a,b) \Rightarrow f\text{ decreasing on }[a,b]f′(x)<0 on (a,b)⇒f decreasing on [a,b]Open formulaOpen in sectionRelatedFormulaf′′(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 IOpen formulaOpen in section