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# 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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