HW4 solution Section 14534 Dūflp ک1 11 wso f has maxi um rate of change along the gradient direction ᶋ ࡏᶆ ҂ / p = 12 x y.y DN i.DE 6.9 Rate of change 1 11 111 6 ⊉ = ݢӞ ࡎಷ P ˙ ݗ! 2 4.4 114 E ଚ Since f so , f is increasing up in the Ù direction 381 a p = ҁ ᤰ ᶆ ҂ 1 p ই ওஞ کӞ۹ ҂ hp ӣ ҁ 3 1 1 pH ԫஞ - 2
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HW4 solution
Section14534Dūflp1ک11wsof has maxi um rate of change along thegradient direction
ᶋ ᶆ҂/p҅ࡏ = 12x y.y DNi.DE6.9Rate of change 111 1116⊉ ݢ=Ӟ ࡎ ಷ P ˙ݗ
!2 4.4114
E ଚSince f so , f is increasing up in
the Ù direction
381 a p =ҁᤰ҅ᶆ҂1pইওஞ҅ک
Ӟ۹ ҂ hpӣ ҁ 3 1
1pH ԫஞ- 2 ྒ
b Rat of change
D嶍ಲӞ ⊉ · 11韷1111
C assume u is Vector as required
then rate of change along u is
鰯 f = 1111 11ᅩ11 cos 45
ԫ ݸ ҅ 1 ޙԫ ݸ
47 FCX.yzixztzxy.lyڊ (p = ҁڕ4̔#܄ 442ு
ԧ҅ নڝڝ bin
19 10 5
The tangent plane at p9 զ 2 110 y D 5෭ -1 0
qxtloy 5Z 33
section 146
6 ௪ ጬӾᬦy3ྲ - y)
2o 3ྲ2yᕁ҂ஞஞ
Ԇ-6cxzyinvwtI 6cut 2W 2 w vݞ
㊳ӣ3lxzyiczwt3cx-zyic-DWW- bcx-zgilw.MN)6 W_w 2 W_W hD