Formula

Tags

• Differential calculus
• Derivative
• Theorem
• Mean value theorem (MVT)

Detail

Variables

• $a$Point or real constant
• $b$Interval endpoint or constant
• $c$Intermediate point (MVT, Rolle)
• $f$Function
• $f'$Derivative of $f$

Related topics

• Mean value theorem

Related formulas

• Related

  Formula

  $$f\text{ is continuous at }[a,b],\ f\text{ is differentiable at }(a,b) \Rightarrow \exists c\in(a,b): f'(c)=\frac{f(b)-f(a)}{b-a}$$
  Open formulaOpen in section

• Related

  Formula

  $$f'(x)=0\ \forall x\in I \Rightarrow f\text{ constant on }I$$
  Open formulaOpen in section