ECO 5405 Lecture Notes - Lecture 5: Oni
1122
EloSoS
Lechre
Notes
is
fkrentiable
at
ae
Zf
X a X a Jarivative
of
*
at
a.
Delc)
or
dfla
exsts
dx
a Flx)- Cla)-
f'la)lx-a)=0
X-a
la)+f'la)
(x-a)
fla)+f'(al(x
-a)
Lin
(,
R
Ae
Lin
TR",
A)
A:R°>
R
A(X+y)=
AAx
+
Ay
(e.,e)
s
ha
standard
basi
of
R
Ax
X A
Document Summary
Elosos lechre notes is fkrentiable at ae z f. Jarivative of * at a . exsts a. , e ) s ha standard basi of r. A e , , ) shndard basis of rr. Vi, ae; j ehinitbm: let us r be n on sat. ae u, f : 0> " . f. Del) : totas desivahe f f der ivate: : Dela) f at a . a n (r r) w s. t. V h h ath e u flash) fla) +0fla):h + e(a) wh. Lemma. f is dferenhable at , h en 0e (a) is uniqve. Ovher", v e r t fla+ th) = fla)+ 0fla) bl+ e (ta) Teath)-fta7 t90 on i hm: 1 daerenhable a t a, hen we say h e x fla) + /fla) (x-a) he e vniqve. Ik k mapin9 est asgne apximahn of f a t a , 1+ 5 affine a lox im a tm for whrch.
