2-4 Rates of Change and Tangent Lines Quick Check

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AP Calculus AB
2-4 Learning Check (with review)
P or NP
Calculus expert’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‘œπΆ ) and instantaneous rates of change (πΌπ‘…π‘œπ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  x  ο€½ x  1
________
over the interval  0,3 ?
(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  x  ο€½ 9 ο€­ x2 at x ο€½ 2 ?
(A) y ο€½
1
9
x
4
2
(D) y ο€½ 4 x ο€­ 3
(B) y ο€½ ο€­4 x  13
________
(C) y ο€½ ο€­4 x ο€­ 3
(E) y ο€½ 4 x  13
OVER οƒ 
3.
Let f  x  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 – 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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