Home/Differential Calculus/Mean value theorem/ConsequencesSection 7.3ConsequencesFormulaCopy 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 IView detail →FormulaCopy LaTeXf′(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 IView detail →FormulaCopy LaTeXf′(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 IView detail →
FormulaCopy 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 IView detail →
FormulaCopy LaTeXf′(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 IView detail →
FormulaCopy LaTeXf′(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 IView detail →