Extreme Value Theorem

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The extreme value theorem states that a continuous function on a closed interval has both a maximum and minimum value.

Extreme 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.


Continuous Function: A continuous function is function with no jumps, gaps, or undefined points.
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
  • Integral
  • Chain Rule
  • Intermediate Value Theorem
  • Critical Point
  • Limit
  • Definite Integral
  • Maximum
  • Discontinuity
  • Mean-Value Theorem
  • First Derivative Test
  • Minimum
  • Fundamental Theorems of Calculus
  • Newton's Method
  • Implicit Differentiation
  • Riemann Sum
  • Indefinite Integral
  • Second Derivative Test
  • Inflection Point