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Sullivan 04 apcalc4e 45342 ch02 166 233 5pp August 7, 2023 12:54

Chapter 2 • Review Exercises 233

8. If the function Free-Response Question
2
2ax + bx − 1 if x ≤ 3 11. The velocity of an object moving on a line is
f (x) = 2
bx + bx − a if x > 3 modeled by a differentiable function v, where v is
measured in meters and t ≥ 0 is measured in
is continuous for all real numbers x, then
minutes. The velocity of the object is observed at
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(A) 19a − 15b = 1 (B) 18a − 9b = 1 several times t and posted in the table below.
(C) 19a − 9b = 1 (D) 19a + 15b = 1
t 0 2 3 6 8
v(t) 0 4 13 7 5
9. Find the slope of the line tangent to the graph
of f (x) = 2x ln x at the point (1, 0). (a) Using the data in the table, approximate v (5).
′
(A) 0 (B) 1 (C) 2 (D) 4 (b) Interpret the meaning of v (5). Be sure to
′
include the correct units.
10. An object moving on a line is modeled by the
position function
3
4
2
s(t) = 3t − 8t − 6t + 24t t > 0
where s is in feet (ft) and t is in seconds (s). Find
the acceleration of the object when its velocity is
zero.
2
2
2
(A) −24 ft/s , 36 ft/s , and 72 ft/s only
2
(B) 36 ft/s only
2
2
(C) 36 ft/s and 72 ft/s only
2
2
(D) −24 ft/s and 36 ft/s only

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