Concavity And The Second Derivative Test Worksheet With Answers Page 4
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9nd
Calculus Maximus
WS 3.4: Concavity & 2
Deriv Test
[ ]
_____ 11. The function f is continuous on the closed interval
3,5 and twice differentiable on the open
( )
( )
( )
( )
f ′
′′
= and
< on the open interval
interval
3,5 . If
3,5 , which of the followign
4
2
f
x
0
could be a table of values for f ?
( )
( )
( )
(A)
(B)
(C)
f x
f x
f x
x
x
x
3
2.5
3
2.5
3
3
4
5
4
5
4
5
5
6.5
5
7
5
6.5
( )
( )
(D)
(E)
f x
f x
x
x
3
3
3
3.5
4
5
4
5
5
7
5
7.5
5
4
=
+
+
_____ 12. For what values of x does the graph of
y x
5
x
11
have a point of inflection?
x = − only
(A)
4
x = − only
(B)
3
x =
(C)
only
0
x =
x = −
(D)
and
0
4
x =
x = −
(E)
0
and
3
( )
3
2
=
−
−
+
_____ 13. Let f be the function defined by
f x
2
x
3
x
12
x
18
. On which of the following
intervals is the graph of f both increasing and concave down?
⎛
⎞
⎛
⎞
1
1
(
)
(
)
(
)
−∞ −
−
−
(A)
, 1
(B)
1,
(C)
1, 2
(D)
, 2
(E)
2,∞
⎜
⎟
⎜
⎟
⎝
2
⎠
⎝
2
⎠
Page 4 of 9
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