Name ______
Hour _____ Date ______
Halloween Activity
Calculus
Work each problem. Then write the answers as an ordered pair (a, b) and follow the instructions for graphing on the sheet provided.
Right Eye
1.a.What is the value at which there isb.At what value is there a
a vertical asymptote of removable discontinuity in
??
2.a.b.Find
3.a.Evaluate: b.Solve:
Plot the points from #1, 2, 3, and connect the points.
Left Eye
4.a.What is the instantaneous rate ofb.Find when x = 1
change of when x = -2?
5.a.Find when x = -2b.Find the average rate of change
of on the interval [-1, -2].
6.a.What is the leading coefficient ofb.Solve:
?
Plot the points from #4, 5, 6, and connect the points.
Nose
7.a.What is the derivative of b.Evaluate:
where ?
8.a.Find the slope of b.Evaluate:
at (3, -4) and multiply it by .
9.a.What is the slope of ab.What is the slope of a line
horizontal line?perpendicular to ?
Plot the points from #7, 8, 9, and connect the points.
Mouth
10.a.Find the derivative of b.What is the opposite of the
at (1, 2). Answer: slope of at (-1, 3)?
11.a.Find the derivative of b.Evaluate:
when x = 1 and divide your answer
by -4.
12.a.Evaluate: b.Solve:
13.a.Find the derivative of b. Find the derivative of .
when ; round your answer toWhat is the coefficient of your
the nearest whole number.answer?
Plot the points from #10, 11, 12, 13, and connect the points in order.
It is Halloween night, Charlie Brown and Linus are trying to catch the Great Pumpkin as
it rises from the pumpkin patch to bring all good calculus students presents and candies.
Linus and Charlie spot the Great Pumpkin just starting to rise at a distance of 80 feet from them.
If the angle of elevation is changing at a rate of per second…
a.How fast is the altitude of the Great Pumpkin changing when the Great Pumpkin is 6 feet off of the ground?
b.How fast is the distance from Charlie Brown and Linus to the Great Pumpkin changing When the Great Pumpkin is 6 feet off of the ground?
c.If Charlie Brown and Linus can run at a rate of 20 feet per second, can they catch the Great Pumpkin before it gets out of their reach of 6 feet?
d.Explain your answer to part c