2008-200的学平第一学期《高等数学D(英语)》期水季试试卷(A卷)-一3 4.Graph Analysis 5.Applications Analysis function f(x)=x+2x3-3x2: 1)(8 marks)Calculate the area of the region which is enclosed by functions 1)(3 marks)Write out all roots of f(x)if there exist; y-cosx and y1. 2)(3 marks)Write out all relative extreme points of f(x)if there exist, 2)(11 marks)A 3-m ladder is leaning against a wall.If the top of the ladder slips 3)(3 marks)Write out all inflection points of f(x)if there exist; down the wall at a constant rate of 0.3m/s, a)What is the rate function of the foot moving away from the wall,where the independent variable of the function is the distance between the bottom and the wall? b)What is the exact figure of the rate when the top is I m above the ground. 4)(3 marks)Write out the increase and decrease intervals of f(x); 5)(3 marks)Write out the concave up and concave down intervals of f(x) 3)(8 marks)A closed rectangular container with a square base is to have a volume of 6)(3 marks)Write out the infinite behaviors of f(x) 1000 cm'.It costs twice as much per square centimeter for the top as it does for the sides and bottom.Find the dimensions of the container of least cost. 7)(5 marks)Sketch the figure of the function2008-2009 学年第一学期《高等数学 D（英语）》期末考试试卷（A 卷）--3 4. Graph Analysis Analysis function 4 32 fx x x x () 2 3 =+ − : 1) (3 marks) Write out all roots of f x( ) if there exist; 2) (3 marks) Write out all relative extreme points of f x( ) if there exist; 3) (3 marks) Write out all inflection points of f x( ) if there exist; 4) (3 marks) Write out the increase and decrease intervals of f x( ) ; 5) (3 marks) Write out the concave up and concave down intervals of f x( ) 6) (3 marks) Write out the infinite behaviors of f x( ) 7) (5 marks) Sketch the figure of the function 5. Applications 1) (8 marks) Calculate the area of the region which is enclosed by functions y x = cos and 2 y x| |1 π = − . 2) (11 marks) A 3-m ladder is leaning against a wall. If the top of the ladder slips down the wall at a constant rate of 0.3m/s, a) What is the rate function of the foot moving away from the wall, where the independent variable of the function is the distance between the bottom and the wall? b) What is the exact figure of the rate when the top is 1 m above the ground. 3) (8 marks) A closed rectangular container with a square base is to have a volume of 1000 cm3 . It costs twice as much per square centimeter for the top as it does for the sides and bottom. Find the dimensions of the container of least cost