Worksheet 3.3 - Increasing, Decreasing, And 1st Derivative Test - Calculus Maximus Page 4
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5Calculus Maximus
WS 3.3: Inc, Dec, and 1st Deriv Test
Short Answer
7. For each of the following, find the critical values (on the indicated intervals, if indicated.) Remember, a
critical value MUST be in the domain of the function, though it may not be in the domain of the
derivative.
2
sin
x
x
[
]
( )
(
)
( )
( )
2
π
=
−
=
=
(a)
f x
x
3
x
(b)
f x
,
0, 2
(c)
f x
2
2
+
−
1 cos
x
x
9
8. Determine the local extrema of each of the following functions (on the indicated interval, if indicated).
Be sure to say which type each is. Justify (this means write a sentence.)
1
[
]
( )
( )
( )
2
π
=
= +
(a)
f x
cos 2
x
,
0, 2
(b)
f x
x
x
2
−
−
x
3
x
4
[
]
( )
( )
2
π
=
+
=
(c)
f x
sin
x
sin
x
,
0, 2
(d)
f x
−
x
2
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