AP Pre- Calculus Unit 1 D2 - Tables & Concavity

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Tables + Concavity (1.1, 1.4) HW
1. Which of the following tables could correspond with a function that has all of the following attributes.
I) /(x) has a global maximum value o16
11) The overage rate of change of f (x) over the interval I -1,2 I is zero .,,,
111) The rate of change of f(x) is positive for all x E (- 00 , 1)
IV) The rate of change of / (x) is negative for all x E ( 1, 00)

(A)><,;j (B)/


I I /(x)
-3
-2
-1
5
0
6 I I
1
8
2
6
6
0

(C) )( ~;v (D)>"-


I I f(x)
-3
-5
-1
-4
0
0
1
I I
6
2
-4
-1
5
2
5
4
1
6
-1



2. Tommy is removing manure from a pile on his uncle's farm. He begins at 8 AM and removes the manure
at a constant rote until noon. He then stops for an hour so that he can eat lunch (after carefully washing
his hands). He begins again at 1 PM and removes manure at a constant rote until the pile is empty at
4 PM. Let M(t) be the volume ;;t"manure, measured in tons, lettin the pile t hours after Tommy begins
working. If Tommy works more slowly ofter lunch than before lunch, which of the following tables could
depict the situation? kJ
-o,, (A) ,C... \, '2. Y-- (B)
0 5 7 8 0 2 6 7 8
I M~t) I 6 1· 4~8 I t6 I 3.6 I 2\ I 1.2 0 11 M(t) I 6 3.6 I 2~4 I 2~4 1.4 0.6 0

- o.f -o.~ (D) ·IX,.
t 0 2 5 6 7 8 0 4 5 6 7 8
M(t) 6 4.2 2.4 2.4 1.6 0.8 0 I M~t) I 6 1 4~5 I 3 I 3 I 2 1 0
•A




3. Tammy is removing manure from o pile on her aunt's form. She begins at 8 AM and removes the manure
until noon. As she works that morning, she gets more efficient, so the rote at which she removes manure
speeds up throughout the morning. At noon, Tammy stops tor on hour so that she can eat lunch (after
carefully washing her hands). She begins again at 1 PM and removes manure until the pile is empty at
4 PM. After lunch, Tammy is tired, so the rote at which she removes manure slows throughout the
ofternoc);;. Let M(t) be the volume of manure, measured in tons, left in the pile t hours ofter Tammy
begins working. Which of the following tables could depict the situation? @
-•·' -1,l(A) - l,'l,. ···" O,'\ .,:,(Bl -,(,.
5
-M-~t-)-+--~-+-l-s-\-j-~---~--t-1-/8---i r--~--tl 1-I-M-~t-)---~-+-l-4-\--1-l-3-\-\~3-.6-+--2-\-.....-~--1

-1.1, .,45(C).><,... ••.? ·e-'-'(D))<...
5
I--M-'--~t-)-+--~'--+-l-3-\-+l-/-4-+-l-2-\-+-1~-2-+--~--1l l1--M-,-~t-)-t--~-1-l-3-\-+l-2-\---il-2'-.8-+-l....:..\-+-~--i




CBHS AP Precalculus 2025/26 - Unit 1, Day 2 HW