Home/Differential Calculus/Mean value theorem/Mean value theorem (MVT)Section 7.2Mean value theorem (MVT)FormulavizCopy LaTeXf is continuous at [a,b], f is differentiable at (a,b)⇒∃c∈(a,b):f′(c)=f(b)−f(a)b−af\text{ is continuous at }[a,b],\ f\text{ is differentiable at }(a,b) \Rightarrow \exists c\in(a,b): f'(c)=\frac{f(b)-f(a)}{b-a}f is continuous at [a,b], f is differentiable at (a,b)⇒∃c∈(a,b):f′(c)=b−af(b)−f(a)View detail →FormulaCopy LaTeXf(b)=f(a)+f′(c)(b−a)f(b)=f(a)+f'(c)(b-a)f(b)=f(a)+f′(c)(b−a)Equivalent form of the MVT.View detail →
FormulavizCopy LaTeXf is continuous at [a,b], f is differentiable at (a,b)⇒∃c∈(a,b):f′(c)=f(b)−f(a)b−af\text{ is continuous at }[a,b],\ f\text{ is differentiable at }(a,b) \Rightarrow \exists c\in(a,b): f'(c)=\frac{f(b)-f(a)}{b-a}f is continuous at [a,b], f is differentiable at (a,b)⇒∃c∈(a,b):f′(c)=b−af(b)−f(a)View detail →
FormulaCopy LaTeXf(b)=f(a)+f′(c)(b−a)f(b)=f(a)+f'(c)(b-a)f(b)=f(a)+f′(c)(b−a)Equivalent form of the MVT.View detail →