Worksheet 3.3 - Increasing, Decreasing, And 1st Derivative Test - Calculus Maximus Page 2
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5Calculus Maximus
WS 3.3: Inc, Dec, and 1st Deriv Test
⎛
⎞
4
x
( )
2
=
+
−
3. Let
f x
x
⎜
4
x
⎟
.
⎜
⎟
5
⎝
⎠
( )
′
_____ (i) Which of the following is
f x
?
(
)(
)
( )
2
2
′
=
+
−
(A)
f x
1
x
5
x
(
)(
)
( )
2
2
′
=
+
−
(B)
f x
1
x
4
x
(
)(
)
( )
2
2
′
=
−
+
(C)
f x
1
x
5
x
(
)(
)
( )
2
2
′
=
−
+
(D)
f x
1
x
4
x
(
)(
)
( )
2
2
′
=
−
−
(E)
f x
1
x
4
x
_____ (ii) Find the open interval(s) on which f is increasing.
(
) (
)
−∞ − ∪
∞
(A)
, 2
2,
(
) (
)
−∞ −
∪
∞
(B)
,
5
5,
(
)
−
(C)
2, 2
(
) (
)
−∞ − ∪
∞
(D)
, 1
1,
(
)
−
(E)
1,1
(
)
(
)
( )
( )
2
2
′
=
+
−
+
_____ 4. The derivative of a function f is given for all x by
f x
2
x
4
x
16 1
g
x
where g is
some unspecified function. At which value(s) of x will f have a local maximum?
(
)
2
( )
( )
2
=
Note:
g
x
g x
x = −
(A)
4
x =
(B)
4
x = −
(C)
2
x =
(D)
2
x = −
(E)
4, 2
Page 2 of 5
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