nw
7
1.
f(x,y)
xy2
3r(t)
(2
t2
+
3)
4.
let
f(x,y)
xe*Y
and
P
(3,9)
angle
of
45.
Of
(y2,2xy)
r'(t)
(t,3t27
calc
11pH):
fx(x,y)
(2x
2
1)cex
*)
fy(x,y)
-
xex
-
3
use
chain
rule
to
evaluate
of
(r(t)
@
t
=
1.5
Vfp
((2(3)
1)(e32
q).
(z)e
4-((2.9
1)(ei),
-3e7
(19,-3)
frc
+
)
"f(rce):
((t)2,22t2.-37
(+4,
+
5)
↑
f(x)
v'(t)
(tY
+
5).(t,3t2y
+
3
t
(1.5)
+
3(1.5)
=
68.344
use
chain
rule
to
evaluate
f(r(+1)
&t
=
-1.8
sin,tic.
St,xthy:
t4+
19:
caissigs:
-213668
s.
in
man
in
2.
calculate
the
gradient
g(x,y)-
y
fy(0,10,21)
0
cOS
(0
2i)
0
axos
y
ei
?
09
&
f(x)
axg(x)
xxy2
x
9x
2x
Duf(p):
118
fall
cosO
Not(cosso):
Fo()
=
-g
(ie,
ch
9.
1
*5
=
-
31
**
-
44
x
5
28
3.
Calculate
the
gradient
h(x,y,2)
xyz7
-n
(yz,xz
,
xxyz
87
of
y
-
2x
32(
2x)
+
x
6(
2x)
3)
2x)2
0
m(t)
=
(v
l)'
fz(0,10,21)
=
(OS
10
21)
1
6.
find
a
fan
f(x,y,
2)
such
they
of
is
the
constant
rector
(2,3,22
10.2
inning
x
-x
7e7x
6
3eby
2e
z
f(x,y,z)
7x
3y
2z
C
12.
f(x,y
7.
find
the
critical
points
of
f(x,y)
8y"
x2
xy
3y2
y3
(3y
4)(y
b)
0rzy
-
4x
y
-
43,6
fx
2x
y
0
fy
32y3
by
3y2
x
0
into
"""
e
2564
x
12x
12x2
+
256x3
12x2
+
13x
-
12(
-
Y3)
+
28
=
44703fxx
=
2
-
local
max
x(-
256x2
12x
13)
0
-
x
0
x
4x
=
for
y-c00r
e
-210)
0,
2(1)
=,
-2(5)
22
13.
find
crit
points
of
fxn
f(x,y)
x
+
2y24y
+
2
x
g(x,y)
x2
-16xy
y
(0,0)
(-
,
)
(,)
AC
-
B
use
the
2nd
derivative
test
to
determine
local
min,
max,
I
saddle
fxx
2
fxy
1
fyy
=
96y2
-
by
6
-
=
2x
20x
-
1
-y
4y
4
=
y
1
(-1,1)
&
(0,0)
&
(-
i,)
09
8
-
16x
1
0x
ib
est,
in
a
road
an
his
is
in
an
e
sit,
is
