Activity 1.6.4.
This activity builds on our experience and understanding of how to sketch the graph of \(f'\) given the graph of \(f\text{.}\)
In the provided figure, we given the respective graphs of two different functions \(f\text{,}\) 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 1.6.2 that connect the behaviors of \(f\text{,}\) \(f'\text{,}\) and \(f''\text{.}\) For instance, write something such as
\(f'\) is on the interval , which is connected to the fact that \(f\) is on the same interval , and \(f''\) is on the interval.
but of course with the blanks filled in. Throughout, view the scale of the grid for the graph of \(f\) as being \(1 \times 1\text{,}\) and assume the horizontal scale of the grid for the graph of \(f'\) is identical to that for \(f\text{.}\) If you need to adjust the vertical scale on the axes for the graph of \(f'\) or \(f''\text{,}\) you should label that accordingly.
