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Unit Gradient
fn
i i
f
Plooflet Fct bea parametrizahoof f c
What is
dat fCrTIt is 0We do not change
geheight when
mooing along f c
Now use thechain rule
Tf crit D I CH so
t
LAG
farcy 7 thy2
ty2
1
came
rTtkEaI
I 3
1h 3D
farcy i 21 9
is a surface
f It yEy
THEE
I
F tamp6fGy 2 fast bytetf
E
9IN
to
a tbytczd2
tpgna
D
x72y2tEE4
Find the
tangent planeat A Chill
Or
If EEE
Tfa HI
Lz
Thang2x thy 22
d
plug in Atl
8
D onD
dentate
Dff tf.v
directionalderivative
for the
for thedirection I
unit vectorIntakes
Slope in thedirection 8
Ft ample
Empief 4500 x y2F LIE
forgo 10,20
Buf Cairo
Ei D Eid
2.20 Lys
2
main
we are goingdown the
a.fncrenkedh.DEflag
Tf I'd
fx
fxslope when
omoving in the1 directionEast
DepIf GigAid
as E
In whichdirection do
we have to
move to
increase f
most
used in
machine leaning
down
iiiX
Laridae
DEF
f
directional
famethe gradient
Ff VIFfl
f
I v s Iinnuitor
FEE
Ffl is themaximalshe is
Steepness
And if we
go in the
dire chore ofthe gradientthe slope is
Ffl
I sIDuft
Ff Tfffllulosd
a Tfl cost
I Tff
1
ofun.tlVfLnff e3
Ffl is themaximal
me
T.fpointscepwadsa.ws
k 0
then we
are on the
topnett
weekExtrema