Use the Taylor series about x = a to verify the familiar "second derivative test" for a maximum or minimum point. That is, show that if f ′ ( a ) = 0 , then f ′ ′ ( a ) > 0 implies a minimum point at x = a and f ′ ′ ( a ) < 0 implies a maximum point at x = a Hint: For a minimum point, say, you must show that f ( x ) > f ( a ) for all x near enough to a .
Use the Taylor series about x = a to verify the familiar "second derivative test" for a maximum or minimum point. That is, show that if f ′ ( a ) = 0 , then f ′ ′ ( a ) > 0 implies a minimum point at x = a and f ′ ′ ( a ) < 0 implies a maximum point at x = a Hint: For a minimum point, say, you must show that f ( x ) > f ( a ) for all x near enough to a .
Use the Taylor series about
x
=
a
to verify the familiar "second derivative test" for a maximum or minimum point. That is, show that if
f
′
(
a
)
=
0
,
then
f
′
′
(
a
)
>
0
implies a minimum point at
x
=
a
and
f
′
′
(
a
)
<
0
implies a maximum point at
x
=
a
Hint: For a minimum point, say, you must show that
f
(
x
)
>
f
(
a
)
for all
x
near enough to
a
.
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
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