3.1 Class Notes - March 27 Lecture HWK #7 due April 5/6...

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March 27 Lecture HWK #7 due April 5/6 7.4: 5, 12, 13, 16, 27 8.2: 2, 14 8.4: 2, 14, 19, 24 Problem (a) Find all the critical points, (b) Use the second derivative test to determine if they are local max or min Find the open intervals on which the function is (c) increasing, (d) convex 53 54 xx x −+ f(x) = x 5 /5 – 5x 3 /3 + 4x 42 2 2 32 '( ) 5 4 ( 1)( 4) ( 2)( 2) ''( ) 4 10 =4 ( 2.5) critical points 2, 1,1, 2 " 32 20, 4 10, 4 32 20 max min max min convex when 2.5 or - 2.5 fx x x x x x x fx x x x x f x =− + = =+ + −− + − + ↑↓ >< 0 x < f(x) = x 5 /5 – 5x 3 /3 + 4x crit. pts. -2,-1,1,2 (2.5) ½ = 1.58 -5 -4 -3 -2 -1 0 1 2 3 4 5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Max and min don’t always alternate 42 2 3 () 3 5 15 15 15 ( 1) 60 30 critical points 1,0,1 '' 30,0,30 max, ?, min increasing 1, 1 decreasing 1 x x x x x x x f x =−= + <− > −<< f(x) = 3x 5 –5x 3 -6 -4 -2 0 2 4 6 -1.5 -1 -0.5 0 0.5 1 1.5
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Max-Min word problem The San Diego zoo is going to build an enclosure for birds. It will have height h and the base will be an r by r square. Suppose they have 300 square feet of fencing. What is the largest volume they can enclose? x rr h Max r 2 h when r 2 + 4rh = 300 23 2 2 300 300 44 300 3 '0 4 when 10, 200 / 40 5 '' 6 / 4 0 so this is a maximum r hV r h r r V rh Vr −− == = = =− < Name that substitution
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).

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3.1 Class Notes - March 27 Lecture HWK #7 due April 5/6...

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