Solution of Assignment # 2
MTH301 (Spring 2012)
Total marks: 10
Lecture # 7 to 15
Question # 1
Find the directional derivative of 2
(, ) ln
f
xy y x at P(1,4) in the direction of
33aij .
Solution:
(, ) (, )
xy
f
fxyifxyj
2ln
y
f
iyxj
x
16
(1, 4) ln 1
1
f
ij
i
i
ˆ()/2uij
ˆ
./2
u
Df fu
Question # 2
Find a unit vector in the direction in which function 22
(, )
f
xy x y
increases most
rapidly at P(4, -3}. .
Solution:
A function increases most rapidly in the direction of the gradient vector
f
at P.
22
(, )
f
xy x y
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