Home/Differential Calculus/Consequences/Formula7.3. ConsequencesFormulaIn 7.3. ConsequencesFormulaCopy LaTeXf′(x)=0 ∀x∈I⇒f constant on If'(x)=0\ \forall x\in I \Rightarrow f\text{ constant on }If′(x)=0 ∀x∈I⇒f constant on ITagsDifferential calculusDerivativeTheoremConsequencesVariablesxxxIndependent variablefffFunctionf′f'f′Derivative of fffRelated topicsMean value theoremFound an error? Contact us.Related formulasRelatedFormulaf(b)=f(a)+f′(c)(b−a)f(b)=f(a)+f'(c)(b-a)f(b)=f(a)+f′(c)(b−a)Open formulaOpen in sectionRelatedFormulaf′(x)>0 ∀x∈I⇒f strictly increasing on If'(x)>0\ \forall x\in I \Rightarrow f\text{ strictly increasing on }If′(x)>0 ∀x∈I⇒f strictly increasing on IOpen formulaOpen in sectionRelatedFormulaf′(x)<0 ∀x∈I⇒f strictly decreasing on If'(x)<0\ \forall x\in I \Rightarrow f\text{ strictly decreasing on }If′(x)<0 ∀x∈I⇒f strictly decreasing on IOpen formulaOpen in section