ep4 - 92.131 Calculus 1 Geometry of Functions For Questions...

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92.131 Calculus 1 Geometry of Functions For Questions 1-4: i) On what intervals is the function ) ( x f increasing? Decreasing? ii) What are the relative extrema? iii) On what intervals is the function ) ( x f concave up? Concave down? iv) What are the points of inflection? v) What is the equation of the line tangent to the graph of ) ( x f at 1 = x ? 1) 2 4 2 1 4 1 ) ( x x x f + = 2) 4 ) ( 2 + = x x x f 3) x e x x f 2 3 ) ( = 4) x x x f ln ) ( 4 = 5) Consider the function x x x x f 9 3 ) ( 2 3 = . a) Find the intervals of increase or and decrease. b) Find the local maximum and minimum values. c) Find the intervals of concavity and any points of inflection. 6) Let x e x x f 2 ) ( = . a) Determine intervals on which f is increasing and decreasing. b) Determine all relative extrema of f . c) Determine intervals on which f is concave up and concave down. d) Determine any inflection points of f . 7) Let x e x x f = 4 ) ( . a) Determine intervals on which f is increasing and decreasing. b) Determine all relative extrema of f . c) Determine intervals on which f is concave up and concave down. d) Determine any inflection points of f . 8) Suppose that 1 3 2 3 4 1 ) ( 2 3 4 + + = x x x x f a) On what intervals is the function ) ( x f increasing? Decreasing? b) On what intervals is the function ) ( x f concave up? Concave down? c) What are the points of inflection? (If, any.) d) What is the equation of the line tangent to the graph of ) ( x f at 1 = x ?
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92.131 Calculus 1 Geometry of Functions x -6 -4 -2 0 2 4 6 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Solutions: 1) 2 4 2 1 4 1 ) ( x x x f + = i) Increasing for x > 0, and decreasing for x < 0 ii) Relative min at x = 0 of 1. iii) Concave up everywhere. iv) Since concavity never changes, there are no points of inflection. v) Since 4 3 ) 1 ( = f and 2 ) 1 ( = f , 4 5 2 = x y 2) 4 ) ( 2 + = x x x f i) Increasing on ) 2 , 2 ( , Decreasing on ) , 2 ( ) 2 , ( −∞ U .
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This note was uploaded on 02/13/2012 for the course MATH 92.131 taught by Professor Staff during the Fall '09 term at UMass Lowell.

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ep4 - 92.131 Calculus 1 Geometry of Functions For Questions...

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