Home/Differential Calculus/Derivative and geometric interpretation/DifferentiabilitySection 4.4DifferentiabilityFormulaCopy LaTeXf is differentiable at a⇒f is continuous at af\text{ is differentiable at }a \Rightarrow f\text{ is continuous at }af is differentiable at a⇒f is continuous at aView detail →FormulaCopy LaTeXf′(a) exists ⇔limh→0f(a+h)−f(a)h exists (finite)f'(a)\text{ exists } \Leftrightarrow \lim_{h\to0}\frac{f(a+h)-f(a)}{h}\text{ exists (finite)}f′(a) exists ⇔h→0limhf(a+h)−f(a) exists (finite)View detail →
FormulaCopy LaTeXf is differentiable at a⇒f is continuous at af\text{ is differentiable at }a \Rightarrow f\text{ is continuous at }af is differentiable at a⇒f is continuous at aView detail →
FormulaCopy LaTeXf′(a) exists ⇔limh→0f(a+h)−f(a)h exists (finite)f'(a)\text{ exists } \Leftrightarrow \lim_{h\to0}\frac{f(a+h)-f(a)}{h}\text{ exists (finite)}f′(a) exists ⇔h→0limhf(a+h)−f(a) exists (finite)View detail →