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4.1 Extreme Value Theorem

4.1 Extreme Value Theorem. f(c)≥f(x) for ALL x in D. f(c)≤f(x) for ALL x in D. f(c)≥f(x) for x near c. f(c)≤f(x) for x near c. EXTREMA. ABS MAX. REL MAX. Point of Inflection. REL MAX. ABS MIN. REL MIN. HW 4-1A Pg. 184 #7-10 all. Critical Numbers (or Critical Points):.

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4.1 Extreme Value Theorem

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  1. 4.1 Extreme Value Theorem

  2. f(c)≥f(x) for ALL x in D f(c)≤f(x) for ALL x in D f(c)≥f(x) for x near c f(c)≤f(x) for x near c

  3. EXTREMA

  4. ABS MAX REL MAX Point of Inflection REL MAX ABS MIN REL MIN

  5. HW 4-1A Pg. 184 #7-10 all

  6. Critical Numbers (or Critical Points): A point, c, in the domain of f at which either f’(c)=0 or f’(c) DNE.

  7. Example 2: Find the critical numbers of each function.

  8. Extreme Value Theorem:If f is ____________ on a ____________ interval [a, b],then f has _______________________________________________on the interval. Continuous Closed Both an absolute maximum and an absolute minimum

  9. Corollary to EVT: The [absolute] extrema will occur at (1) or (2) An endpoint A critical point

  10. Candidate Test for Absolute Extrema: Find the critical points (where f’ = 0 or f’ DNE) Test endpoints (a and b) and CP into f

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