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Maxima and Minima

To find maximum and minimum values of function f (x)
  • Find f ′(x) and take f ′ (x) = 0 and find the roots.
  • Then find f ′′ (x) for each of these roots.
     
    If f ′′ (a) > 0, f (a) is minimum value of f (x)
     
    If f ′′ (a) < 0, f (a) is maximum value of f (x)
     
    If f ′′ (a) = 0, f (a) is not maximum or minimum value.
     
    Curl F = ∆ × F = Description: 621.png
     
    Grad f = f = Description: 626.png
     
    div F = Description: 631.png




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