MAT 124 Jones - Fall 2004
Calculus I
Exam 4
Place all solutions neatly on a separate sheet of paper; solutions written on the exam may not be
graded. Show all work for partial credit! Clearly write ID# - no names - on each sheet of paper
you turn in to be graded.
1. Differentiate the following functions:
(a)
(b)
(c)
(d)
2. A catenary is the curve formed by a homogeneous flexible cable hanging from two
points under its own weight. If the lowest point of the catenary is the point (0,a), it can
be shown that an equation of it is . Show that a catenary is
concave upward at at each of its points. (That is, show that for all x.)
3. A ladder 25 feet long is leaning against a vertical wall. If the bottom of the ladder is
pulled horizontally away from the wall at a rate of 3 ft/sec, how fast is the top of the
ladder sliding down the wall when the bottom of the ladder is 15 feet from the wall?
4. (a) Find the absolute extrema for on .
(b) Find the absolute extrema for on .
