ASSIGNMENT 3
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, September
26. The online assignment will close at 9:00 a.m. on Friday, September 26.
Special instruction: In this assignment, calculate all derivatives using the definition of derivative (and not,
for example, the Power Rule).
1. For what values of a and b is the line −2x + y = b tangent to the curve y = ax3 when x = −5?
2. Let
(
f (x) =
1
x
x−
3 2
2
+
3
4
if x ≤ 1
.
if x > 1
Prove that f 0 (1) = −1.
3. Let b < a2 . Prove that there are exactly two lines tangent to y = x2 which pass through the point (a, b).