Home/Differential Calculus/Increasing and decreasing/Formula8.1. Increasing and decreasingFormulaIn 8.1. Increasing and decreasingFormulaCopy LaTeXf′(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]TagsAnalysisIncreasing and decreasingDifferential calculusDerivativeVariablesxxxIndependent variableaaaPoint or real constantbbbInterval endpoint or constantfffFunctionf′f'f′Derivative of fffFound an error? Contact us.Related formulasRelatedFormulaf′(x)>0 on (a,b)⇒f increasing on [a,b]f'(x)>0\text{ on }(a,b) \Rightarrow f\text{ increasing on }[a,b]f′(x)>0 on (a,b)⇒f increasing on [a,b]Open formulaOpen in sectionRelatedFormulaf′′(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 section