# 2-4 Rates of Change and Tangent Lines Quick Check

AP Calculus AB
2-4 Learning Check (with review)
P or NP
Calculus expertβs name is: ________________________
NO CALCULATOR SHOW ALL WORK (even for multiple choice)
STOP, DROP, AND AP!!
ο·
ο·
1.
I can calculate average rates of change (π΄πππΆ ) and instantaneous rates of change (πΌπππΆ )
I can find equations of tangent lines and normal lines to a curve at a given point
Which of the following values is the average rate of change for f ο¨ x ο© ο½ x ο« 1
________
over the interval ο¨ 0,3ο© ?
(A) ο­3
2.
(B) ο­1
(C) ο­
1
3
(D)
1
3
(E) 3
Which of the following is an equation for the tangent line to f ο¨ x ο© ο½ 9 ο­ x2 at x ο½ 2 ?
(A) y ο½
1
9
xο«
4
2
(D) y ο½ 4 x ο­ 3
(B) y ο½ ο­4 x ο« 13
________
(C) y ο½ ο­4 x ο­ 3
(E) y ο½ 4 x ο« 13
OVER ο
3.
Let f ο¨ x ο© ο½ 2 x ο­ x 2 .
(a) Find the instantaneous rate of change at x ο½ 3
(b) Find the equation of the tangent line at x ο½ 3
REVIEW β The following two questions are from the 2003 AP Calculus AB Exam
4.
5.
________
For x ο³ 0 , the horizontal line y ο½ 2 is an asymptote for the graph of function f .
Which of the following statements must be true?
________
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