Which two of the following conditions will be satisfied when a [differentiable] function is
increasing
on an interval
(
a
,
b
)
\displaystyle {\left({a},{b}\right)}
(
a
,
b
)
?
f
′
(
x
)
≤
0
\displaystyle {f}'{\left({x}\right)}\leq{0}
f
′
(
x
)
≤
0
for all
x
\displaystyle {x}
x
in
(
a
,
b
)
\displaystyle {\left({a},{b}\right)}
(
a
,
b
)
.
f
(
x
1
)
>
f
(
x
2
)
\displaystyle {f{{\left({x}_{{1}}\right)}}}>{f{{\left({x}_{{2}}\right)}}}
f
(
x
1
)
>
f
(
x
2
)
when
a
<
x
1
<
x
2
<
b
\displaystyle {a}<{x}_{{1}}<{x}_{{2}}<{b}
a
<
x
1
<
x
2
<
b
.
f
′
(
x
)
≥
0
\displaystyle {f}'{\left({x}\right)}\geq{0}
f
′
(
x
)
≥
0
for all
x
\displaystyle {x}
x
in
(
a
,
b
)
\displaystyle {\left({a},{b}\right)}
(
a
,
b
)
.
f
(
x
1
)
<
f
(
x
2
)
\displaystyle {f{{\left({x}_{{1}}\right)}}}<{f{{\left({x}_{{2}}\right)}}}
f
(
x
1
)
<
f
(
x
2
)
when
a
<
x
1
<
x
2
<
b
\displaystyle {a}<{x}_{{1}}<{x}_{{2}}<{b}
a
<
x
1
<
x
2
<
b
.
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