WORKSHEET 2  Fall 1995
1. For each graph below of a function
f
(
x
), sketch a graph of its derivative
f
(
x
):
a)
b)
c)
d)
e)
f)
g)
h)
i)
2. Without using the concept of a limit (and thus derivative), write the equations of all lines through the
point (
a, a
2
) which intersect the curve
y
=
x
2
exactly once. Which of these is the tangent line? Would
this process work to determine the tangent lines for any curve? If so, why? If not, give a counterexample.
3.
Rectilinear motion
is motion of an object along a straight line. Examples of such motion are objects
falling under the pull of gravity, a dragster racing along a straight line course, or an airplane flying at
level flight along a straight line path.
Suppose we have an equation which gives the position of a moving object along a straight line with
respect to some reference point labeled 0. Let
s
(
t
) = 16
t
2
denote the number of feet an object has fallen under the pull of gravity after
t
seconds has passed from
the first moment it was first let go.
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 Spring '08
 Grether
 Calculus, Equations, Derivative, Vector Space, Velocity

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