First Derivative Test

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The first derivative test is a method for determining the maximum and minimum values of a function using its first derivative.

First derivative test 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.


Critical Point: A critical point is a point in the graph of a function where the derivative is either zero or undefined.
Derivative: A derivative is the infinitesimal rate of change in a function with respect to one of its parameters.
Maximum: The maximum of a set, function, etc. is the largest value attained by that object.
Minimum: The minimum of a set, function, etc. is the smallest value attained by that object.

Classroom Articles on Calculus I (Up to College Level)

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