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Cell["Calculus: The Language of Change", "Title"],
Cell[TextData[{
StyleBox["Exercise Set 9.2\n",
FontVariations->{"Underline"->True}],
"Graphs Without Formulas"
}], "Subtitle"],
Cell["by John Robeson", "Subsubtitle"],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Exercise 1) Rough Sketch", "Subtitle"]], "Subtitle"],
Cell["\<\
Make a qualitative rough sketch of a graph of the distance traveled as a \
function of time on the following hypothetical trip:\
\>", "Text"],
Cell["(a) You travel a total of 100 miles in 2 hours.", "Text"],
Cell["\<\
(b) Most of the trip is on rural interstate highway at the 65 mph speed \
limit. What qualitative feature or shape does the graph of distance vs. time \
have when speed is 65 mph?\
\>", "Text"],
Cell["\<\
(c) You start from your house at rest, gradually increase your speed to 25 \
mph, slow down, and stop at a stop sign.\
\>", "Text"],
Cell["\<\
(d) What shape is the graph of distance vs. time while you are stopped?\
\>", "Text"],
Cell["\<\
(e) You speed up again to 25 mph, travel a while, and enter the interstate. \
At the end of the trip, you exit, slow to 25 mph, stop at a stop sign, and \
proceed to your final destination.\
\>", "Text"],
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Cell["(a) You travel a total of 100 miles in 2 hours.", "Text"],
Cell[CellGroupData[{
Cell["Solution to (a)", "Subsection"],
Cell["\<\
Our graph of distance vs. time should start at (0, 0) and end at (2, 100), \
where (0, 0) is the start of the trip at your house and (2, 100) is our \
destination 100 miles away after 2 hours.\
\>", "Text"]
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Cell["\<\
(b) Most of the trip is on rural interstate highway at the 65 mph speed \
limit. What qualitative feature or shape does the graph of distance vs. time \
have when speed is 65 mph?\
\>", "Text"],
Cell[CellGroupData[{
Cell["Solution to (b)", "Subsection"],
Cell[TextData[{
"Recall that speed is ",
Cell[BoxData[
\(distance\/time\)]],
". So our speed at any instant is \nreflected in the slope of our distance \
vs. time graph. Therefore, for this portion of the trip our graph should be \
a straight line with a positive slope of 65 ",
Cell[BoxData[
\(miles\/hour\)]],
"."
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(c) You start from your house at rest, gradually increase your speed to 25 \
mph, slow down, and stop at a stop sign.\
\>", "Text"],
Cell[CellGroupData[{
Cell["Solution to (c)", "Subsection"],
Cell["\<\
As stated in part (a) our graph starts at (0, 0). The slope at this point is \
0 since initially we are stopped and our speed is zero. The graph then \
curves upward until our slope becomes 25 mph. The graph continues upward \
linearly at this rate until we begin to slow down, at which time the graph \
curves to a flat section for the time we are stopped.\
\>", "Text"]
}, Open ]]
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Cell["(d)", "Section"],
Cell["\<\
(d) What shape is the graph of distance vs. time while you are stopped?\
\>", "Text"],
Cell[CellGroupData[{
Cell["Solution to (d)", "Subsection"],
Cell["\<\
As indicated in part (c), the graph is flat when we are stopped, since our \
speed, and hence the slope of our graph, is zero.\
\>", "Text"]
}, Open ]]
}, Closed]],
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Cell["(e)", "Section"],
Cell["\<\
(e) You speed up again to 25 mph, travel a while and enter the interstate. \
At the end of the trip, you exit, slow to 25 mph, stop at a stop sign, and \
proceed to your final destination.\
\>", "Text"],
Cell[CellGroupData[{
Cell["Solution to (e)", "Subsection"],
Cell["\<\
Again, our graph curves upward from a slope of zero to a slope of 25 mph and \
continues at this rate until we enter the interstate at which time the graph \
curves upward more until our slope becomes 65 mph. It is linear at this \
slope of 65 mph until we exit and the graph curves again to a slope of 25 \
mph, then curves even more to a flat section when we are again stopped. The \
final section of our graph ends at the coordinate (2, 100) where our slope is \
again zero (stopped).\
\>", "Text"],
Cell["\<\
Note that our graph is always going up or is flat since we never go \
backwards, but of course, the slope changes many times and is much steeper at \
65 mph than at 25 mph.\
\>", "Text"]
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