Which two of the following conditions will be satisfied when a [twice differentiable] function is
concave up
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
)
\displaystyle {f}'{\left({x}\right)}
f
′
(
x
)
is decreasing on the interval
(
a
,
b
)
\displaystyle {\left({a},{b}\right)}
(
a
,
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
)
\displaystyle {f}'{\left({x}\right)}
f
′
(
x
)
is increasing on the interval
(
a
,
b
)
\displaystyle {\left({a},{b}\right)}
(
a
,
b
)
.
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