ASSIGNMENT 16 for SECTION 001
This assignment is to be handed in. There are two parts: Part A and Part B.
Part A will be graded for completeness. You will receive full marks only if every question has been completed.
Part B will be graded for correctness. You will receive full marks on a question only if your answer is correct
and your reasoning is clear. In both parts, you must show your work.
Please submit Part A and Part B separately, with your name on each part.
Part A
From Calculus: Early Transcendentals:
From section 4.5, complete questions: 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50
Part B
1. Sketch the graph of a single function f satisfying all of the following criteria:
x = 0, y = 1 and y = 2 are asymptotes;
f 0 (x) < 0 for x ∈ (−∞, 0) ∪ (2, ∞), and f 0 (x) > 0 for x ∈ (0, 2);
f 00 (x) < 0 for x ∈ (−∞, 0) ∪ (0, 4), and f 00 (x) > 0 for x ∈ (4, ∞); and
f (2) = 4.
2. State and sketch the graph of a function which is concave up on the intervals (2n, 2n + 1) (for all integers
n) and concave down on the intervals (2n + 1, 2n + 2) (for all integers n).
3. (a) Find a nonlinear polynomial function which is decreasing everywhere.
3. (b) Sketch the graph of the function in part (a).
4. Recall the solution to Question 4 in Assignment 1: given a, b and c such that: (i) their average is 2/3;
and (ii) a = 1 + b, c can be any real number. Let P be the product abc, where a, b and c satisfy the
same criteria. Write P as a function of c, and sketch the graph of the function. (You may use without
justification the solution to Question 4 in Assignment 1.)
5. Consider an 8.5” × 11” sheet of paper folded such that the
bottom right-hand corner touches the top edge, as shown.
Find the smallest possible length of the crease c.
c