Worksheet 3.3 - Increasing, Decreasing, And 1st Derivative Test - Calculus Maximus
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5Calculus Maximus
WS 3.3: Inc, Dec, and 1st Deriv Test
Name_________________________________________ Date________________________ Period______
Worksheet 3.3—Increasing, Decreasing, and 1st Derivative Test
Show all work. No calculator unless otherwise stated.
Multiple Choice
_____ 1. Determine the increasing and decreasing open intervals of the function
( ) (
) (
)
4 / 5
1/ 5
=
−
+
f x
x
3
x
1
over its domain. Tip: factor out least powers from the derivative to
put it into full-fledged-factored-form!
⎛
⎞
⎛
⎞
1
1
− −
−
∞
(A) Inc:
1,
, Dec:
,
⎜
⎟
⎜
⎟
⎝
5
⎠
⎝
5
⎠
⎛
⎞
⎛
⎞
1
1
(
)
− −
∪
∞
−
(B) Inc:
1,
3,
, Dec:
,3
⎜
⎟
⎜
⎟
⎝
5
⎠
⎝
5
⎠
(
) (
)
(
)
−∞ − ∪
∞ , Dec:
−
(C) Inc:
, 1
3,
1,3
⎛
⎞
⎛
⎞
1
1
(
)
−∞ −
∪
∞
−
(D) Inc:
,
3,
, Dec:
,3
⎜
⎟
⎜
⎟
⎝
5
⎠
⎝
5
⎠
⎛
⎞
⎛
⎞
1
1
(
)
(
)
−
∪
∞
−
∪
∞
(E) Inc:
,3
3,
, Dec:
1,
3,
⎜
⎟
⎜
⎟
⎝
5
⎠
⎝
5
⎠
( )
π
π
= −
− ≤ ≤ . Determine all open interval(s)
_____ 2. Let f be the function defined by
f x
x
cos 2 ,
x
x
on which f is decreasing.
π
π
π
π
⎛
5
⎞ ⎛
7
11
⎞
−
−
(A)
,
,
,
⎜
⎟ ⎜
⎟
⎝
⎠ ⎝
⎠
12
12
12 12
π
π
π
π
⎛
⎞ ⎛
⎞
5
11
−
−
(B)
,
,
,
⎜
⎟ ⎜
⎟
⎝
12
6
⎠ ⎝
6 12
⎠
π
π
π
π
⎛
⎞ ⎛
⎞
5
3
11
−
−
(C)
,
,
,
⎜
⎟ ⎜
⎟
⎝
12
8
⎠ ⎝
8
12
⎠
π
π
π
π
⎛
⎞ ⎛
11
⎞
−
−
(D)
,
,
,
⎜
⎟ ⎜
⎟
⎝
6
12
⎠ ⎝
6 12
⎠
π
π
⎛
⎞ ⎛
⎞
5
7
π
π
− −
(E)
,
,
,
⎜
⎟ ⎜
⎟
⎝
12
⎠ ⎝
12
⎠
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