ASSIGNMENT 17 for SECTION 001
Part A is to be completed online before 7:00 a.m. on Friday, March 25. Part B and Part C, which require
full solutions, are to be handed in at the beginning of class on the same date.
Part A [10 marks]
This part of the assignment focuses on fundamental skills and computations. It can be found online, labelled
A17, at webwork.elearning.ubc.ca — sign in using the MATH110 001 2010W button.
Part B [5 marks]
This part of the assignment is drawn directly from the course texts. It focuses on mathematical exposition;
you will be graded primarily on the clarity and elegance of your solutions.
From the Calculus: Early Transcendentals text, complete questions 12 and 30 from section 4.3.
Part C [15 marks]
This part of the assignment consists of more challenging questions. You are expected to provide full solutions
with complete arguments and justifications.
1. Sketch the curve x3 + y 3 − 3xy = 0, indicating all extrema and points of inflection. Be sure to show all
your work. (Hint: this is not a function.) For a bonus mark, identify the name of this curve.
2. The function
1 −x/2
xe
,
8
defined on the interval x > 0, is an example of a Gamma function, a probability density function used to
model waiting times — for example, the probability at birth (vertical axis) of a given lifespan (horizontal
axis). Sketch the graph of the function, indicating all extrema and points of inflection.
f (x) =
3. Propose a function G modelling your grade on the final exam with respect to the number h of hours
you spend studying between now and then. Sketch G(h), indicating all extrema, points of inflection and
asymptotes. Explain each of these features of your function (e.g. explain why the graph is concave up on
a certain interval).