Calculus

Critical Points

Extrema and saddle points

  • University
  • about 4 min
  • 5 of 31 in the family
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MaxMinf(x)f′(x)
f(x)=x3−3x,f′(x)=3x2−3f(x) = x^3-3x, \quad f'(x) = 3x^2-3

Critical points are where f′(x)=0 (green zeros). If f″>0 → local min (green), f″<0 → local max (pink), f″=0 → inflection (orange).