Formula

Tags

• Differential calculus
• Continuity
• Derivative
• Differentiability
• Derivative formula

Variables

• $a$Point or real constant
• $f$Function

Frequently asked questions

Is every differentiable function continuous?

Yes: if $f$ is differentiable at $a$, then $f$ is continuous at $a$. The converse need not hold (e.g. $|x|$ at $0$).

Related formulas

• Related

  Formula

  $$f'(a)\text{ exists } \Leftrightarrow \lim_{h\to0}\frac{f(a+h)-f(a)}{h}\text{ exists (finite)}$$
  Open formulaOpen in section