First
Derivative
Test
Suppose
f
(
x
)
is
____________________
at
x
=
c
and
____________________
to
the
left
of
c
on
some
interval
(
a
,
c
)
and
to
the
right
of
c
on
some
interval
(
c
,
b
)
.
If
f'
(
x
)
>0
to
the
____________________
of
x
=
c
and
f'
(
x
)
<0
to
the
____________________
of
x
=
c
,
then
f
has
a
local
____________________
at
x
=
c
If
f'
(
x
)
<0
to
the
____________________
of
x
=
c
and
f'
(
x
)
>0
to
the
____________________
of
x
=
c
,
then
f
has
a
local
____________________
at
x
=
c
