Formula

Tags

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

Explore the idea

Variables

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

Also known as

• teorema del valor medio
• TVM
• mean value theorem

Related topics

• Mean value theorem

Related formulas

• Related

  Formula

  $$G(x)=\int_a^x f(t)\,dt,$$
  Open formulaOpen in section

• Related

  Formula

  $$f\text{ is continuous at }[a,b],\ f\text{ is differentiable at }(a,b),\ f(a)=f(b) \Rightarrow \exists c\in(a,b): f'(c)=0$$
  Open formulaOpen in section

• Related

  Formula

  $$f(b)=f(a)+f'(c)(b-a)$$
  Open formulaOpen in section