MA 3972-MA-Book April 11, 2018 12:19How to Approach Each Question Type 39- When appropriate, represent the given information in calculus notations. For example,
if it is given that the volume of a cone is decreasing at 2 cm^3 per second, write
dV
dt
=
−2cm^3/
sec. Similarly, represent the quantity being sought in calculus notations. For
example, if the question asks for the rate of change of the radius of the cone at 5 seconds,
write “Find
dr
dt
att=5 sec.”
TIP • Do not forget to answer the question. Free-response questions tend to involve many
computations. It is easy to forget to indicate the final answer. As a habit, always state
the final answer as the last step in your solution, and if appropriate, include the unit
of measurement in your final answer. For example, if a question asks for the area of a
region, you may want to conclude your solution by stating that “The area of the region
is 20 square units.”- Do the easy questions first. Each of the 6 free-response questions is worth the same
amount of credit. There is no penalty for an incorrect solution. - Pay attention to the scales of thexandyaxes, the unit of measurement, and the labeling
of given charts and graphs. For example, be sure to know whether a given graph is that
off(x)orf′(x). - When finding relative extrema or points of inflection, you must show the behavior of the
function that leads to your conclusion. Simply showing a sign chart is not sufficient.
TIP • Often a question has several parts. Sometimes, in order to answer a question in one part of
the question, you might need the answer to an earlier part of the question. For example,
to answer the question in part (b), you might need the answer in part (a). If you are not
sure how to answer part (a), make an educated guess for the best possible answer and
then use this answer to solve the problem in part (b). If your solution in part (b) uses the
correct approach but your final answer is incorrect, you could still receive full or almost
full credit for your work. - As with solving multiple-choice questions, trust your instincts. Your first approach to
solving a problem is usually the correct one.
4.3 Using a Graphing Calculator
- The use of a graphing calculator is permitted in Section I---Part B multiple-choice
questions and in Section II---Part A free-response questions. - You are permitted to use the following 4 built-in capabilities of your graphing calculator
to obtain an answer:- plotting the graph of a function
- finding the zeros of a function
- calculating numerically the derivative of a function
- calculating numerically the value of a definite integral
For example, if you have to find the area of a region, you need to show a definite inte-
gral. You may then proceed to use the calculator to produce the numerical value of the
definite integral without showing any supporting work. All other capabilities of your cal-
culator can only be used tocheckyour answer. For example, you may not use the built-in
[Inflection] function of your calculator to find points of inflection. You must use calculus
showing derivatives and indicating a change of concavity.