There are two parts to this assignment. The first part is on WeBWorK — the link is available on the course
webpage. The second part consists of the questions on this page. You are expected to provide full solutions
with complete justifications. You will be graded on the mathematical, logical and grammatical coherence and
elegance of your solutions. Your solutions must be typed, with your name and student number at the top of
the first page. If your solutions are on multiple pages, the pages must be stapled together.
Your written assignment must be handed in before the start of your recitation on Friday, October
17. The online assignment will close at 9:00 a.m. on Friday, October 17.
1. Determine all of the x-values at which the graph of f (x) =
2. Prove that the curves
x4 − x + 1
has horizontal tangent lines.
x4 + x + 1
+ 2 = 1 and x2 − y 2 = 1 intersect at right angles provided a2 − b2 = 2.
3. This question refers to the 2010 paper “Tidal asymmetry in estuaries with mixed semidiurnal/diurnal
tides” [1]. A copy of the paper is available on the course webpage.
In equation (1) of the paper, the author describes the tidal sea surface elevation ζ(x, t). Fix x = 0, so
that ζ(x, t) is a function solely of t, which we shall denote ζ(t).
(a) Calculate ζ 00 (t).
(b) What does ζ 00 (t) describe? Give your answer in a few sentences.
[1] Nidzieko, N.J. “Tidal asymmetry in estuaries with mixed semidiurnal/diurnal tides.” Journal of Geophysical Research:
Oceans 115 C8 (2010).