Concavity And The Second Derivative Test Worksheet With Answers Page 3
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9nd
Calculus Maximus
WS 3.4: Concavity & 2
Deriv Test
(
)(
)
2
′′ =
−
−
_____ 8. Let f be a function with a second derivative given by
f
x x
4
x
7
. What are the x-
coordinates of the points of inflection of the graph of f ?
(A) 0 only
(B) 4 only
(C) 0 and 7 only
(D) 4 and 7 only
(E) 0, 4, and 7
_____ 9.
( )
A particle moves along a straight line. The graph of the particle’s posittion
x t at time t is
t < < . The graph has horizontal tangents at
t = and
t =
shown above for 0
and a point of
6
1
5
t = . For what values of t is the velocity of the particle increasing?
inflection at
2
t < <
(A) 0
2
t < <
(B) 1
5
t < <
(C) 2
6
t < <
(D) 3
only
5
t < < and 5
t < <
(E) 0
1
6
( )
( )
2
2
′
=
_____ 10. (Calculator Permitted) The derivative of the function f is given by
f x
x
sin
x
. How
(
)
−
many points of inflection does the graph of f have on the open interval
2, 2
?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Page 3 of 9
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