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Any function is

  • increasing at if
  • decreasing at if
  • concave up at if
  • concave down at if

Critical point is the point where . A critical point is

  • maxima where
  • minima where
  • inflection point if and does change sign around

Critical Points

Critical Points are points where Notice that at critical points the function is neither increasing not decreasing.

You can comment on increasing/decreasing on either side of critical points.