Intermediate Value Theorem

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The intermediate value theorem states that if f is continuous on a closed interval [a, b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in [a, b] such that f(x) = c.

Intermediate 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.

Classroom Articles on Calculus I (Up to College Level)

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