friday linfu afforddstaplet/f20/notes/november 6.pdf · 2020. 11. 13. · friday november 6 awe...
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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
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