FRIDAY November 6 awepress records Linfu

affordawLASTTIME turfyandTheorem Thegradient Pf

www.Hnfhfnn.nu

gives a normal vectorto

tommmbhhn

the level suntan flag c

If f Go yo Zola and 171 0yo 2d0

then the level set A level c has

tangent plane

0 175 1 0 yo 2 do x Xo y yo 2 Zo

Thegradient of f can beplotted as a vector field.gthe level curves are perpendicularto the vectors

Exer cise

Let 5Cxy l X y DRAW

in E2 thetheme

admit

fClay Yz

z

Pf Cyill

I

tI

o

SS3ilotterationgDerivatiAKA 2ndDerivation.jo

Suppose fix y is a d function

twice continuouslydifferentiable

then we can take 2nd partial

derivatives

Et Eiffel EFEHIEIox

8 E.co oa.I oqiotai

SOMETIMES we put the 2ndpartial derivatives in a matrix

Of of

I

Called the Hessianmatrix off

7 If f is a CZ Amalia

then OfFoy

DIdyox

also works for 3 variable functions

So it doesn't matterwhator der you

differentiate in

EXAMPLE 0To

ofcx.gl eT

2x e T ftp.i 4yxeK T

1 SAME

ft eyeYf y 4xye

7