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Critical value

  1. Apr 21, 2004 #1
    What is the definition of a critical value of a function?
     
  2. jcsd
  3. Apr 21, 2004 #2
    Main Entry: critical value
    Function: noun

    mathematics : the value of the argument or independent variable corresponding to a critical point of a function
     
  4. Apr 21, 2004 #3
    Main Entry: critical point
    Function: noun

    1 mathematics : a point on the graph of a function where the derivative of the function is zero or infinite
    2 : TRANSFORMATION TEMPERATURE
    3 a : the point on a phase diagram of a pure substance that corresponds to its critical state b : CRITICAL STATE
     
  5. Apr 23, 2004 #4
    The critical point on a graph is a point where:

    1) The derivative of f is equal to zero.
    2) The derivative of f does not exist.
     
  6. Apr 25, 2004 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Did you really copy this correctly? A critical point of a function is one where the derivative is zero or does not exist. That does not necessarily mean "is infinite". The absolute value function f(x)= |x| has a critical point at x=0.
     
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