Hoja de Trabajo 5 Maximos Minimos Intervalo Cerrado - Solucio N
August 6, 2022 | Author: Anonymous | Category: N/A
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Bopcr tcioftn bo Ictoi²ctelc Bopcrtcioftn ctelc Cpaelcbc Cpaelc bc Ictoi² ctelc ctelc 4 (Ictoi²ctelc ctelc 30=) ∔ GE\ELL, GCLRE \oicfc 4
²f Mnjc bo Rrcdcjn Fn. ? - \naulenf n Efstrullenfos: Tosuoavc lcbc ufc bo acs luostenfos quo so ao prosoftcf c lnftefucle²nf bojcfbn lnfstcflec bo tnbn prnlobeieoftn y rcznfcieoftn molmn. Gcvnr bo oftrohcr su trcdcjn of mnjcs tcicˑfn fn lcrtc bodebciofto ofhrcpcbcs o ebofteffilcbcs lnf su fnidro, f²uiorn uiorn bo lcrfot, golmc, lursn y solle²nf. nf.
\oreo 3 (Lnfloptns) 3 (Lnfloptns) Botoriefcr se acs sehueoftos prnpnselenfos snf vorbcborcs n snf gcascs; bo sor gcascs justeffiquo su rospuostc. 3. Oa f² uiorn uiorn l os uf i²ijfein ijfein anlca anlc a bo bo g g se se oxesto uf eftorvcan cdeortn (c, (c, d) quo lnfteofo c l c l tc tcaa quo g (l) ≯ g (x) ∀x ∍ (c, d). quo T: Gcasn, uiorn l os uf i²ijfein anlc anlcaa bo bo g g se se oxesto uf eftorvcan cdeortn (c, (c, d) T: Gcasn, puostn quo oa f²uiorn l quo lnfteofo c c l tca quo g quo g ((l) ≢ g (x) ∀x ∍ (c, d) .
4. \e \e g (l) 9 0 oftnflos of l of l mcy uf i²cxein cxein anlca bo ac gufle²nnf f g . T: Gcasn, lucfbn g (l) 9 0, g 0, g fn fn foloscreciofto teofo uf i²cxein cxein anlca of of l . T: Gcasn, puostn quo lucfbn
\oreo 4 4 (Nporctnrec) c 3. Botoriefcr ans puftns lr² lr²ijtelns bo acs sehueoftos guflenfos: c ) h (x) 9 x 2 ∔ =x4 . 37x h (x) 9 2x< ∔ 37 x
h (x) 9 2x(x4 ∔ 2)
0 9 2x(x4 ∔ 2) x 9 0 x 9 0
x4 ∔ 2 9 0
x 9 ³4
x 9 ∔4, x 9 0 y x x 9 9 4. d ) m(x) 9 sef4(x) + lns(x lns(x).
m (x) 9 4 se sef( f(x x)lns( )lns(x x) ∔ sef( sef(x x) 0 9 sef(x sef(x)[4 lns lns((x) ∔ 3Y sef(x sef( x) 9 0
4 ln lns(x) ∔ 3 9 0 3 sef(x sef( x) 9 0 lns(x) 9 4 Rnbns ans vcanros vcanros bnfbo oa sef( sef(x x) 9 0, 3 π πf y πf y oa lns(x lns(x) 9 , 4πf ³ . 4 < π x 9 9 π πf f y x x 9 9 4πf ³ , f ∍ Z. <
3
Mnjc bo Rrcdcjn ? ∔ Ictoi² ctelc 4 (Ictoi² ctelc 30=)
l ) g (x) 9
2x . x4 + 3
g (x) 9
2( 2(x x4 + 3) ∔ 2x(4 (4x x) (x4 + 3)4 4
4
g (x) 9 2x + 2 ∔ =x (x4 + 3)4 ∔2x4 + 2 09 4 (x + 3)4 0 9 ∔2x4 + 2 2 x4 9 2 x 9 ³3 x 9 ∔3, x 9 3 . 4. _delcr _delcr ans oxtroins cdsnautns cdsnautns bo ac gufle² nf nf of oa eftorvcan lorrcbn bcbn: c ) g (x) 9 < ∔ x,
[∔3, 4Y.
3) Oflnftrcr puftn(s) lr lr²²ijteln ijtelns. s. g (x) 9 ∔3. Fn mcy puftn lr²ijteln. ijte ln.
4) Ovcaucr Ovcaucr ans oxtro oxtroins ins boa efto eftorv rvcan can lorrcbn. g (∔3) 9 < ∔ (∔3) y g g (4) (4) 9 < ∔ 4. g (∔3) 9 2 y y g (4) (4) 9 3.
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