AP Calculus AB
Scoring Guide
Unit 3 Progress Check: FRQ Part B
Copyright © 2017. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or
in print beyond your school’s participation in the program is prohibited.
Page 1 of 8
1.
NO CALCULATOR IS ALLOWED FOR THIS QUESTION.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly
label any functions, graphs, tables, or other objects that you use. Justifications require that you
give mathematical reasons, and that you verify the needed conditions under which relevant
theorems, properties, definitions, or tests are applied. Your work will be scored on the
correctness and completeness of your methods as well as your answers. Answers without
supporting work will usually not receive credit.
Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your
answer is given as a decimal approximation, it should be correct to three places after the
decimal point.
Unless otherwise specified, the domain of a function is assumed to be the set of all real
numbers for which
is a real number.
Consider the curve given by the equation
.
(a)
Show that
.
Please respond on separate paper, following directions from your teacher.
(b)
Write an equation for the line tangent to the curve at the point
.
Please respond on separate paper, following directions from your teacher.
(c)
Evaluate
at the point
.
Please respond on separate paper, following directions from your teacher.
(d)
The point
is on the curve. Find the value of
.

AP Calculus AB
Scoring Guide
Unit 3 Progress Check: FRQ Part B
Copyright © 2017. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or
in print beyond your school’s participation in the program is prohibited.
Page 2 of 8
Please respond on separate paper, following directions from your teacher.