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Mathematics
Mathematics
Problem
Which of the following conditions on a differentiable function
f
f
f
at
x
=
c
x=c
x
=
c
guarantees that
f
(
c
)
f(c)
f
(
c
)
is a local minimum? a)
f
′
(
c
)
=
0
and
f
′
′
(
c
)
<
0
f'(c)=0\text{ and }f''(c)<0
f
′
(
c
)
=
0
and
f
′′
(
c
)
<
0
b)
f
′
(
c
)
=
0
and
f
′
′
(
c
)
=
0
f'(c)=0\text{ and }f''(c)=0
f
′
(
c
)
=
0
and
f
′′
(
c
)
=
0
c)
f
′
(
c
)
=
0
and
f
′
′
(
c
)
>
0
f'(c)=0\text{ and }f''(c)>0
f
′
(
c
)
=
0
and
f
′′
(
c
)
>
0
d)
f
′
(
c
)
>
0
and
f
′
′
(
c
)
=
0
f'(c)>0\text{ and }f''(c)=0
f
′
(
c
)
>
0
and
f
′′
(
c
)
=
0
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