AP Calculus AB Quiz
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ANALYTICAL APPLICATIONS OF DIFFERENTIATION
Question 1
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A function
f
f
f
has a local maximum at
x
=
−
2
x=-2
x
=
−
2
and a local minimum at
x
=
1
x=1
x
=
1
; which could be
f
′
f'
f
′
?
A
f
′
f'
f
′
is negative for
x
<
−
2
x<-2
x
<
−
2
, positive for
−
2
<
x
<
1
-2<x<1
−
2
<
x
<
1
, negative for
x
>
1
x>1
x
>
1
.
B
f
′
f'
f
′
crosses the
x
x
x
-axis at
x
=
−
2
x=-2
x
=
−
2
and
x
=
1
x=1
x
=
1
, positive for
x
<
−
2
x<-2
x
<
−
2
, negative for
−
2
<
x
<
1
-2<x<1
−
2
<
x
<
1
, positive for
x
>
1
x>1
x
>
1
.
C
f
′
f'
f
′
is zero only at
x
=
0
x=0
x
=
0
and is positive everywhere else.
D
f
′
f'
f
′
is positive for
x
<
−
2
x<-2
x
<
−
2
, negative for
x
>
−
2
x>-2
x
>
−
2
, and never zero again.
E
f
′
f'
f
′
is negative for all
x
x
x
and has holes at
x
=
−
2
x=-2
x
=
−
2
and
x
=
1
x=1
x
=
1
.
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