CalculusI_recitation-7

# CalculusI_recitation-7 - Calculus I Recitation Session #7...

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Calculus I Recitation Session #7 ( § 4.1 and § 4.2) Summary of important concepts § 4.1 [1] Relative (local) maximum and relative (local) minimum (a) ( ) f c is a local maximum if it is the greatest for all x from a small neighborhood of c (top of hill) ( ) f c is a local minimum if it is the smallest for all x from a small neighborhood of c (bottom of valley) (b) A property of local minimum/local maximum If ( ) f x has a local maximum or minimum value at an interior point of its domain and ( ) f x is continuous at c , then either '( ) 0 f c = or '( ) f x is undefined at c . Meanwhile, x c = is called a critical point of ( ) f x . Note: This property says local maximum or minimum only occur at a critical point. [2] Absolute maximum and absolute minimum (a) ( ) f c is an absolute maximum over its domain if ( ) ( ) f x f c for all x in its domain (highest point). ( ) f c is an absolute minimum over its domain if ( ) ( ) f x f c for all x in its domain (lowest point). (b) The Extreme Value Theorem: Make sure the function ( ) f x is continuous over a closed interval before applying the theorem. (c) How to find the absolute maximum/absolute minimum? (i) Find all critical points of ( ) f x . (ii) Evaluate ( ) f x at the critical points as well as the end points of the closed interval. (iii)

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## This note was uploaded on 09/02/2010 for the course MATH SMUD 206 taught by Professor Condon during the Spring '10 term at UMass (Amherst).

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CalculusI_recitation-7 - Calculus I Recitation Session #7...

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