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Second Derivative Test

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The second derivative test is a method for determining a function's maxima, minima, and points of inflection by using its first and second derivatives.

Second 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.

Prerequisites

Derivative: A derivative is the infinitesimal rate of change in a function with respect to one of its parameters.
Inflection Point: An inflection point is a point on a curve at which the concavity changes.

Classroom Articles on Calculus I (Up to College Level)

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