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Chapter 3-Higher Order Derivatives
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Notes for chapter 3 of multivariable calculus. Easy to read! Student-made notes clarifying difficult concepts. Includes diagrams and tricks for exams and quizzes.
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Higher Order Derivatives :3 1 .
:
Iterated Partial Derivatives
Of :
of Equality of Partial Derivatives
Oxdy dydx
of (o Yo) 1 (S(DX DY)
WM
:
,
and Xo + DX
between Xo
,
OXdY BXDY eX
S(DX DY)
(1x Yo + DY)
- Yo
:
, , ,
= of (x , Y) DXDY
dydX
3 2 .
:
Taylor's Theorem
f( % o + h) =
f(Yo) +
hio) + Ri , ) First-order Taylor's Theorem
R
, (o 2) ,
=
+(xo n)-, f(xo)-(Df(o)](n)
↑ o + h) =
/Ito) +
Shilhini(o) + Ro Second-order Taylor's There is
account for
of, ofoa
3
.3 :
Extrema of Real-valued Functions
First-Derivative Test :
Df(o) 0 =
shows critical points
Second-Derivative Test :
Hessian : HEYolIn) : Tox Moshin ; matrix
esymmetric
I Moxi.... Ooo()
ha]
-
h, ...
flox
:
· flexnox
=
(1) (IXn](nxn](nx1] :
[17 Scalar output
Hf(Yo)(n) >0 >
-
minimum
HF(X)(5) <0 >
-
maximum
2-variables :
minimum :
I .
(Xo , Yo)
= ( Y ,
2 .
Of(X Yo ,
3
. D
( )-l0@(0 40
=
,
maximum :
(o Yo
= ( Y.
1 .
, ,
2 .
Of(X You ,
.
3 D
( )-l0@(0 40
=
,
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