MAT1339 C Fall 2014 Assignment 2 Due: October 22 Instructor: Camelia Karimianpour Instructions: You should show your work for multiple choice questions. For long questions you should write all the steps, similar to what we did in class. You can work in a group but you should write your own assignments. You are not allowed to copy another student’s work. Note that plagiarism is taken very seriously at the University of Ottawa. This assignment is worth 5% of your final grade. Question 1 (2 marks) Find the value of k such that x = 2 is a critical 1 number of f (x) = x4 − 3x2 + kx. 4 1. 4 2. 5 2 3. 2 4. −2 1 Question 2 (2 marks) Find the domain of the function f (x) = p . (x − 1)(x − 3) 1. (1, 3) 2. [1, 3] S 3. (−∞, 1) (3, +∞) 4. (1, +∞) √ √ Question 3 (2 marks) Find all the critical numbers of f (x) = 6 x − x x. 1. x = 0 and x = 1. 2. x = 0 and x = 3. 3. x = 1 and x = 3. 4. x = 0 and x = 2. 2 Question 4 (8 marks) Let f (x) = 14 x4 − 2x2 + 5. Find the absolute maximum value and minimum value of f (x) on [−4, 4]. 3 Question 5 (8 marks) We wish to design an open storage box ( no top) with a square base. The storage box must have a volume of 16 cm3 . The bottom costs $4 per square centimetre and the sides costs $1 per square centimetre. Find the dimensions that will minimize the total cost. What will the minimum cost be? 4 2 −4 . Question 6 (18 marks) Let f (x) = xx2 −9 (a) (3 marks) State the domain, x-intercept(s) and y-intercept(s). (b) (2 marks) Find all the possible horizontal and vertical asymptotes. (c) (2 marks) Find f 0 (x) and f 00 (x). (d) (4 marks) Find all the critical numbers, state all the intervals of increase and decrease, find all the local minimum points and all the local maximum points. (e) (4 marks) Find all the points of inflection, and state intervals of concavity. (f) (3 marks) Sketch the graph. 5 Use this page if you need more space. 6

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