Mean-Value Theorem

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The mean-value theorem states that if f(x) is differentiable on the open interval (a, b) and continuous on the closed interval [a, b], there is at least one point c in (a, b) such that (a - b) f(c) = f(a) - f(b).

Mean-value theorem is a college-level concept that would be first encountered in a Calculus I course. It is an Advanced Placement Calculus AB topic and is listed in the California State Standards for Calculus.


Derivative: A derivative is the infinitesimal rate of change in a function with respect to one of its parameters.

Classroom Articles on Calculus I (Up to College Level)

  • Calculus
  • Indefinite Integral
  • Chain Rule
  • Inflection Point
  • Continuous Function
  • Integral
  • Critical Point
  • Intermediate Value Theorem
  • Definite Integral
  • Limit
  • Discontinuity
  • Maximum
  • Extreme Value Theorem
  • Minimum
  • First Derivative Test
  • Newton's Method
  • Fundamental Theorems of Calculus
  • Riemann Sum
  • Implicit Differentiation
  • Second Derivative Test