MATHEMATICS 120 PROBLEM SET 4
Due October 9, 2002
For full credit, please show all work.
sin x
and g(x) = − cot x. Find all values of x at which f 0 (x)
1 + cos x
and g 0 (x) exist and are equal.
1. (5 marks) Let f (x) =
2. (5 marks) Find all values of a such that the graph of y = sin(ax) cos(ax) has a horizontal
tangent at the point where x = π.
3. (10 marks) Let f (x) = x2 + 4x + 10 cos x. Prove that there is a point a in (π/2, 10π)
such that the line tangent to the graph y = f (x) at the point (a, f (a)) goes through the
origin. (Hint: Find the equation of the tangent line for general a. When does this line go
through the origin? Does this equation have a solution in the given interval?)
Please read Section 2.5 of the textbook and make sure that you can solve problems 1–52 at
the end of the section.
1