ii.:
t,j
!
I
lzi
I
L
Ji
4,6t6
MA
201
Studv Guide for
Test
2
You
need
to
know:
The
graph
of
z
=
f
(x,y)
is a
surface
in 3space'
A
fevel cLlrve
is a
set
of
points
where
f
(x,y)=
some
constant
k.
Must be able
to approach
(a,
b)
from
any direction,
along any
path,
for
/(r,.v)
to
have a limit at (a,
b),
must
have
limit at (a,
b)
to
be
continuous at
(a, b)'
ARule
of
thumb:
ii
t
is
given
by a
formula
in
elementary
functions'
then
f
is
continuous
wherever
it
is
welldefined.
,
..The
Heart of
Calculus
Formula for functions
of multiple variables:
.{{I
+;g)
=./(i)
+
V.f
.;6
(Okay, so you
don't
have
to
actually
know
this,
but
it
sure looks nice.)
rlMaximum
rate
of change
of a function occurs in
direction
of
the
gradient'
.$The
gradieni vecior
is perpendicular
to
level curves
of
the function.
:f
A
continuous
function
on a
closed,
pounded set attains an
absolute
maximum
and
absoluie minimum
on
that
set
.
''
You
need
to
be able
to:
Find
partial
derivatives

differentiate
with
respect
to
one
variable
while treating
the other(s) as constants.
Recognize
and
interpret both
ways
of
writing
partial
derivatives'
:.,.Use
ilairaut's
Theoiem
{and
rernember
to
say that
you
are using
it
and,
if
necessary,
justifY
its
use)
Find
the equation
of
the
plane tangent to the
graph
of
z
=
f
(x,.:')
at
('tto'"1'o
)
'
,,.
.Oraw
a
tree
cliagram(if
you
need
it)
and use the
chain
rule to
find
needed
partials'
Find
the
gradient
vector for
a
function.
Find
the
directional derivative
of
/(t)
at
io
in
the
direction
of
it
'
Find
the maximum
rate of change of
a
function
at
a
point, and
the direction
in
which
it
occurs.
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 Spring '10
 Marples
 Derivative, pts, Gradient

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