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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.

Prerequisites

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