MA125 Calculus I
Exam 3
Name: _________________________________________
There are 6 questions. For full credit, show all steps of your work. A calculator may not be
used.
1. Find the critical points of the following functions.
a.
b.
√
2. Consider the function
Given that
a) Find the critical points of
.
and
,
.
Critical points:
b) Find the intervals where
is increasing and decreasing.
Increasing on these intervals:
Decreasing on these intervals:
c) Find the intervals where
is concave up and concave down.
Concave up on these intervals:
Concave down on these intervals:
(Sketch the function
on the next page.)
d) Sketch the function
. For full credit, show the x and y-intercepts, all extrema, inflection
points and any vertical and horizontal asymptotes.
3. Find the minimum and maximum value of
on the interval
4. A piece of wire of length 100 cm is bent into the shape of a rectangle. Which dimensions produce the
rectangle of maximum area?
5. Find the function satisfying
that goes through the point (-1,5).
6. Evaluate the following limits. Check if L’Hôpital’s Rule is applicable and use the rule if it applies. (If it
doesn’t apply, evaluate the limit using another method.)
a.
b.
c.