Extreme Value theorem and Increasing, decreasing, First Derivative test question: How come when we're determining the absolute/extreme/global maximum or minimum of a function that we substitute c at f(c) not f'(c), even though we're getting our critical points by using first derivative? While when examining relative minimum or maximum, the values of the critical points are plugged in directly towards the differentiated function instead? Reference: Math 31 or Calculus 1(High School Calculus) Reference Topic: Curve Sketching