Some Practice Problems for Exam 2
Applied Calculus I, MA 119
October 15, 2015
The following are some problems which will help you prepare for Exam 2. This is not
a comprehensive list of all possible problems that might be asked. Rather, it is a list of
problems which can help you practice some of the important ideas and techniques which will
be on the exam.
1. Find the derivative of the following functions.
3
5
a) f (x) = 4x3 − 5x2 − 3x + 1
b) g(x) = √ −
x x
5
c) F (x) = 9(3x5 − x3 + 7x)6
d) F (x) =
(1 + 4x2 )3
e) G(x) = 5e6x
f) F (x) = ln(x3 − 1)
4x − 2
g) F (t) = (3t + 5) ln(t)
h) F (x) =
ln(x)
√
2
i) G(t) = 1 + t2
j) F (x) = (2x − 1)ex
√
e3x
l) G(x) = e2x − x
k) F (x) =
2x + 1
√
2
m) F (x) = ln( x2 + 4)
n) G(t) = 2e−t /4
2. Find the equation of the tangent line to the graph of the function f (x) = 2xex at x = 0.
3. Find all values of x for which the tangent line to f (x) =
ex
is horizontal.
x2 − 3
4. a) State the limit definition of the derivative, f 0 (x).
b) Use the limit definition of the derivative to compute f 0 (2) when f (x) = 3x2 − x.
5. Each graph below is a graph of a function y = f (x). For each one, sketch the graph of
the derivative, y = f 0 (x), locating and labeling all x-values where f 0 (x) = 0 on your graph.
For each graph, state the intervals on which f 0 (x) > 0 and the intervals on which f 0 (x) < 0.