ASSIGNMENT 1·8 for SECTION 001
There are two parts to this assignment. The first part is online at www.mathxl.com. The second part
consists of the questions on this page. You are expected to provide full solutions with complete arguments
and justifications. You will be graded on the correctness, clarity and elegance of your solutions. Your answers
must be typeset or very neatly written. They must be stapled, with your name and student number at the top
of each page.
1. Let f (x) = (x − a)2 (x − b)3 + x. Prove that f takes on the value
a+b
for some x.
2
2. There are exactly two lines through the point (1, −3) which are also tangent to the parabola y = x2 .
Sketch the lines and find their equations.
3. We proved in class that for positive integer values of n,
d n
x = nxn−1 .
dx
Prove, using the limit definition of derivative, that for positive integer values of n,
d −n
x = −nx−n−1 .
dx