1.6. THE SECOND DERIVATIVE
61
⊳
Activity 1.17.
This activity builds on our experience and understanding of how to sketch the graph
of f ′ given the graph of f .
f
x
f ′
x
f ′′
x
f
x
f ′
x
f ′′
x
Figure 1.33: Two given functions f , with axes provided for plotting f ′ and f ′′ below.
In Figure 1.33, given the respective graphs of two different functions f , sketch the
corresponding graph of f ′ on the first axes below, and then sketch f ′′ on the second
set of axes. In addition, for each, write several careful sentences in the spirit of those in
Activity 1.15 that connect the behaviors of f , f ′ , and f ′′ . For instance, write something
such as
f ′ is
on the interval
, which is connected
to the fact that f is
on the same interval
,
61
⊳
Activity 1.17.
This activity builds on our experience and understanding of how to sketch the graph
of f ′ given the graph of f .
f
x
f ′
x
f ′′
x
f
x
f ′
x
f ′′
x
Figure 1.33: Two given functions f , with axes provided for plotting f ′ and f ′′ below.
In Figure 1.33, given the respective graphs of two different functions f , sketch the
corresponding graph of f ′ on the first axes below, and then sketch f ′′ on the second
set of axes. In addition, for each, write several careful sentences in the spirit of those in
Activity 1.15 that connect the behaviors of f , f ′ , and f ′′ . For instance, write something
such as
f ′ is
on the interval
, which is connected
to the fact that f is
on the same interval
,