Calculus I 
Test #2

October 22, 2001

Name____________________ 
R. Hammack

Score ______

(1) Suppose
f(x)
= . Use
the limit definition of the derivative
to find f '(x).
(2)
Find the derivatives of the following functions. You may use any applicable
rule.
(a) f(x)
= 4+
3+
(b) f(x)
=
(c) y
= x tan(x)
(d) [
25 + cos( )
] =
(e) [
] =
(3) Suppose f(x)
equals the number of dollars it costs to erect an xfoothigh
transmitting tower.
(a) What are the units of f
'(x)?
(b) Suppose that f
'(100) = 105. Explain, in ordinary English, what this
means.
(4) This problem concerns the function
f that is graphed below
(a) Sketch the graph
of f '(x).
(Use the same coordinate axis)
(b) Suppose g(x)
= sin(f(x)).
Find g '(4).
(c) Suppose h(x)
= 4 + +
f(x). Find
h'(2).
(5) Sketch the graph of a function f whose
derivative has the following properties:
f(0) = 2, f
'(0) = 0, f
'(3) = 0, and f
'(x) ≤ 0 for all values of x.
(6) Consider the function f(x)
= x +
(a) Find the slope of the tangent line
to the graph of f at the point where
x = 4.
(b) Find the equation of the tangent
line to the graph of f at the point
where x = 4.
(7) Find all values of x
for which the slope of the tangent to the graph of y
= sin x at the point x is
(8) Find the slope of the
tangent to the graph of
at the point (π/4, 1).
(9) Suppose a 10footlong ladder is
sliding down a wall in such a way that the base of the ladder moves away from
the wall at a constant rate of 2 feet per second. How fast is the
top of the ladder moving down the wall when it is 6 feet above the floor?