Concavity And The Second Derivative Test Worksheet With Answers
ADVERTISEMENT
1
2
3
4
5
6
7
8
9nd
Calculus Maximus
WS 3.4: Concavity & 2
Deriv Test
Name_________________________________________ Date________________________ Period______
Worksheet 3.4—Concavity and the Second Derivative Test
Show all work. No calculator unless otherwise stated.
Multiple Choice
3
2
a < , the graph of
=
+
+
+ is concave up on which of the following intervals?
_____ 1. If
0
y ax
3
x
4
x
5
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
1
1
1
1
(
)
−∞ −
−∞
−
∞
∞
−∞ −
(A)
,
(B)
,
(C)
,
(D)
,
(E)
, 1
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎝
a
⎠
⎝
a
⎠
⎝
a
⎠
⎝
a
⎠
( )
( )
( )
′
′′
=
=
= , which of the following must be true about the graph of f ?
_____ 2. If
f
0
f
0
f
0
0
(A) There is a local max at the origin
(B) There is a local min at the origin
(C) There is no local extremum at the origin
(D) There is a point of inflection at the origin
(E) There is a horizontal tangent at the origin
5
4
=
−
+
+
_____ 3. The x-coordinates of the points of inflection of the graph of
y
x
5
x
3
x
7
are
(A) 0 only
(B) 1 only
(C) 3 only
(D) 0 and 3
(E) 0 and 1
_____ 4. Which of the following conditions would enable you to conclude that the graph of f has a point
= ?
of inflection at x
c
( )
( )
(A) There is a local max of f ′ at x
′′
′′
=
=
c
(B)
f
c
0
(C)
f
c
does not exist
(D) The sign of f ′ changes at x
=
c =
c
(E) f is a cubic polynomial and
0
Page 1 of 9
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education