ASSIGNMENT 6 for SECTION 001
There are three parts to this assignment. Part A is to be completed online before 7:00 a.m. on Friday,
November 5. 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 can be found online, labelled A6, 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 question 48 and parts (a), (b) and (c) of question
66 from section 3.2.
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. Recall the definitions of even and odd functions from Part C of Assignment 2. Let f be a differentiable
even function. Show that its derivative f 0 (x) is odd.
2. Let n be a positive integer, and f (x) = xn . Prove the following equality:
(x + h)n − xn
= nxn−1 .
h→0
h
lim
(Hint: think about which terms in the expanded numerator will not have a factor h2 ; and see question
71 in section 3.2 of the Calculus: Early Transcendentals text.) Note that this proves that f 0 (x) = nxn−1 .
3. Find the equations of all horizontal lines that are tangent to the curve y = x2 (8 − x2 ).