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Finding Global Extrema definitions

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  • Critical Point
    A location where the derivative equals zero or does not exist, often used to identify potential extrema.
  • Derivative
    A measure representing the slope of the tangent line to a function at a given point.
  • Local Maximum
    A point where a function reaches a highest value compared to nearby points on its graph.
  • Local Minimum
    A point where a function reaches a lowest value compared to nearby points on its graph.
  • Global Maximum
    The absolute highest value a function attains on a specified interval.
  • Global Minimum
    The absolute lowest value a function attains on a specified interval.
  • Extreme Value Theorem
    A principle stating that a continuous function on a closed interval has both a maximum and a minimum value.
  • Closed Interval
    A set of real numbers including all values between two endpoints, with both endpoints included.
  • Endpoint
    A boundary value of an interval where the function is evaluated for extrema.
  • Continuity
    A property where a function has no breaks, jumps, or holes over its domain.
  • Horizontal Tangent
    A tangent line with zero slope, indicating a potential extremum on the graph.
  • Power Rule
    A differentiation technique used to find the derivative of terms with variable exponents.
  • Domain
    The complete set of input values for which a function is defined.
  • Polynomial Function
    An expression involving sums of powers of a variable with constant coefficients.
  • Graph
    A visual representation of a function showing its behavior, extrema, and other features.