ASSIGNMENT 1·11
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 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. Find the equation of the line tangent to the curve y = √
3x
at the point 1, √32 .
x2 + 1
2. You were asked in a workshop to find a polynomial with horizontal tangent lines at x = a, b, c and d.
n
Explain why ((x − a)(x − b)(x − c)(x − d)) , where n is an integer greater than 1, is such a polynomial.
3. A supernova is a stellar explosion. One possible trigger is when a massive star runs out of fuel and
collapses, in a matter of hours, under the force of its own gravity. At that point, material is ejected
outward at high velocity.
Consider a supernova which is ejecting a spherical shell of material radially outward at a velocity equal
to 3% of the speed of light. (Astrophysicists observe similar velocities.) Determine the rate at which the
volume within the spherical shell is expanding.