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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