Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
A continuous function
f
f
f
satisfies
f
(
x
)
>
0
f(x)>0
f
(
x
)
>
0
for
1
<
x
<
4
1<x<4
1
<
x
<
4
,
f
(
4
)
=
0
f(4)=0
f
(
4
)
=
0
, and
f
(
x
)
<
0
f(x)<0
f
(
x
)
<
0
for
4
<
x
<
7
4<x<7
4
<
x
<
7
. Define
F
(
x
)
=
∫
1
x
f
(
t
)
d
t
F(x)=\int_{1}^{x} f(t)\,dt
F
(
x
)
=
∫
1
x
f
(
t
)
d
t
. On which interval is
F
F
F
decreasing? a)
(
1
,
4
)
(1,4)
(
1
,
4
)
only b)
(
1
,
4
)
(1,4)
(
1
,
4
)
and
(
4
,
7
)
(4,7)
(
4
,
7
)
c)
(
4
,
7
)
(4,7)
(
4
,
7
)
only d)
F
F
F
is nowhere decreasing on
(
1
,
7
)
(1,7)
(
1
,
7
)
Browse the problem library