© Scarborough
Math 131
Fall 2007
Quiz 7 KEY
(20pts) NAME (printed neatly): ________________________________
(10pts) Section Number (circle correct section): 502 (10:20am)
503 (11:30am)
506 (4:10pm)
Quiz Grade: ______________
1. (18pts) If g ( x) = 3e x + 5 , give three different functions that are
antiderivatives of g(x).
Here are 3 possible answers:
G(x) = 3ex + 5x
(here C = 0)
H(x) = 3ex + 5x – 7
F(x) = 3ex + 5x + 8
[Any function of the form K(x) = 3ex + 5x + C where C is any real number.]
2. (5pts) Correct the following:
∫ (x
2
)
+ 6 dx =
∫ (x
2
)
+ 6 dx =
x3
+ 6x .
3
x3
+ 6x + C
3
6
⎛
⎞
3. (30pts) Find ∫ ⎜ e − x + + 3x100 ⎟dx apples sold per month where x is the
x
⎝
⎠
number of months after a new advertisement appeared.
⎛
∫ ⎜⎝ e
−x
+
6
3 101
⎞
x + C apples sold
+ 3x100 ⎟dx = −e − x + 6 ln x +
101
x
⎠
© Scarborough
Math 131 Fall 2007 Quiz 7 KEY
2
4. Given the following information about a continuous smooth change-of-rate
function y.
•
•
•
•
•
•
On the interval (–5, –3), y > 0
A relative maximum occurs at x = – 4
A zero occurs at x = –3
On the interval (–3, –2), y < 0
dy
On the interval (–5, –4),
> 0.
dx
dy
On the interval (–4, –2),
< 0.
dx
(17pts – each letter part is worth 1 pt) Circle all statements that must be true
about the accumulation function A(x) given the above information about its
change-of-rate function y.
[bold means it is true]
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
o.
p.
q.
A relative maximum of A(x) occurs at x = –4.
An inflection point of A(x) occurs at x = –4.
A relative minimum of A(x) occurs at x = –4
A relative maximum of A(x) occurs at x = –3.
An inflection point of A(x) occurs at x = –3.
A relative minimum of A(x) occurs at x = –3
A(x) > 0 on the interval (–5, –4)
A(x) < 0 on the interval (–5, –4)
A(x) = 0 on the interval (–5, –4)
A(x) > 0 on the interval (–4, –3)
A(x) < 0 on the interval (–4, –3)
A(x) = 0 on the interval (–4, –3)
A(x) is concave up on the interval (–5, –4)
A(x) is concave down on the interval (–5, –4)
A(x) is concave up on the interval (–4, –3)
A(x) is concave down on the interval (–4, –3)
None of these