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2

2,5 puntos
Dada la función f(x)=ax2+5x+bxf(x) = ax^2 + 5x + \dfrac{b}{x}, responda a las siguientes cuestiones:
i
Calcule los valores de aa y bb para que la función tenga un extremo relativo en el punto (1,4)(1, 4).1,25 pts
ii
Utilizando los valores a=2a = 2 y b=0b = 0, determine la ecuación de la recta tangente a la función f(x)f(x) en el punto de abscisa x=1x = 1.1,25 pts

Formulario

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Tabla de la distribución normal estándar Z∼N(0,1)Z \sim N(0,1) P(Z<k)=12π∫−∞ke−t2/2 dtP(Z < k) = \dfrac{1}{\sqrt{2\pi}}\displaystyle\int_{-\infty}^{k} e^{-t^2/2}\,dt
Densidad de la normal estándar y función de distribución, con el área hasta k sombreada 1 1 0,5 0,5 k k
kk01
−3,50,00020,0002
−3,40,00030,0003
−3,30,00050,0005
−3,20,00070,0007
−3,10,00100,0009
−3,00,00130,0013
−2,90,00190,0018
−2,80,00260,0025
−2,70,00350,0034
−2,60,00470,0045
−2,50,00620,0060
−2,40,00820,0080
−2,30,01070,0104
−2,20,01390,0136
−2,10,01790,0174
−2,00,02280,0222
−1,90,02870,0281
−1,80,03590,0351
−1,70,04460,0436
−1,60,05480,0537
−1,50,06680,0655
−1,40,08080,0793
−1,30,09680,0951
−1,20,11510,1131
−1,10,13570,1335
−1,00,15870,1562
−0,90,18410,1814
−0,80,21190,2090
−0,70,24200,2389
−0,60,27430,2709
−0,50,30850,3050
−0,40,34460,3409
−0,30,38210,3783
−0,20,42070,4168
−0,10,46020,4562
−0,00,50000,4960
kk01
0,00,50000,5040
0,10,53980,5438
0,20,57930,5832
0,30,61790,6217
0,40,65540,6591
0,50,69150,6950
0,60,72570,7291
0,70,75800,7611
0,80,78810,7910
0,90,81590,8186
1,00,84130,8438
1,10,86430,8665
1,20,88490,8869
1,30,90320,9049
1,40,91920,9207
1,50,93320,9345
1,60,94520,9463
1,70,95540,9564
1,80,96410,9649
1,90,97130,9719
2,00,97720,9778
2,10,98210,9826
2,20,98610,9864
2,30,98930,9896
2,40,99180,9920
2,50,99380,9940
2,60,99530,9955
2,70,99650,9966
2,80,99740,9975
2,90,99810,9982
3,00,99870,9987
3,10,99900,9991
3,20,99930,9993
3,30,99950,9995
3,40,99970,9997
3,50,99980,9998
kk23
−3,50,00020,0002
−3,40,00030,0003
−3,30,00050,0004
−3,20,00060,0006
−3,10,00090,0009
−3,00,00130,0012
−2,90,00180,0017
−2,80,00240,0023
−2,70,00330,0032
−2,60,00440,0043
−2,50,00590,0057
−2,40,00780,0075
−2,30,01020,0099
−2,20,01320,0129
−2,10,01700,0166
−2,00,02170,0212
−1,90,02740,0268
−1,80,03440,0336
−1,70,04270,0418
−1,60,05260,0516
−1,50,06430,0630
−1,40,07780,0764
−1,30,09340,0918
−1,20,11120,1093
−1,10,13140,1292
−1,00,15390,1515
−0,90,17880,1762
−0,80,20610,2033
−0,70,23580,2327
−0,60,26760,2643
−0,50,30150,2981
−0,40,33720,3336
−0,30,37450,3707
−0,20,41290,4090
−0,10,45220,4483
−0,00,49200,4880
kk23
0,00,50800,5120
0,10,54780,5517
0,20,58710,5910
0,30,62550,6293
0,40,66280,6664
0,50,69850,7019
0,60,73240,7357
0,70,76420,7673
0,80,79390,7967
0,90,82120,8238
1,00,84610,8485
1,10,86860,8708
1,20,88880,8907
1,30,90660,9082
1,40,92220,9236
1,50,93570,9370
1,60,94740,9484
1,70,95730,9582
1,80,96560,9664
1,90,97260,9732
2,00,97830,9788
2,10,98300,9834
2,20,98680,9871
2,30,98980,9901
2,40,99220,9925
2,50,99410,9943
2,60,99560,9957
2,70,99670,9968
2,80,99760,9977
2,90,99820,9983
3,00,99870,9988
3,10,99910,9991
3,20,99940,9994
3,30,99950,9996
3,40,99970,9997
3,50,99980,9998
kk45
−3,50,00020,0002
−3,40,00030,0003
−3,30,00040,0004
−3,20,00060,0006
−3,10,00080,0008
−3,00,00120,0011
−2,90,00160,0016
−2,80,00230,0022
−2,70,00310,0030
−2,60,00410,0040
−2,50,00550,0054
−2,40,00730,0071
−2,30,00960,0094
−2,20,01250,0122
−2,10,01620,0158
−2,00,02070,0202
−1,90,02620,0256
−1,80,03290,0322
−1,70,04090,0401
−1,60,05050,0495
−1,50,06180,0606
−1,40,07490,0735
−1,30,09010,0885
−1,20,10750,1056
−1,10,12710,1251
−1,00,14920,1469
−0,90,17360,1711
−0,80,20050,1977
−0,70,22960,2266
−0,60,26110,2578
−0,50,29460,2912
−0,40,33000,3264
−0,30,36690,3632
−0,20,40520,4013
−0,10,44430,4404
−0,00,48400,4801
kk45
0,00,51600,5199
0,10,55570,5596
0,20,59480,5987
0,30,63310,6368
0,40,67000,6736
0,50,70540,7088
0,60,73890,7422
0,70,77040,7734
0,80,79950,8023
0,90,82640,8289
1,00,85080,8531
1,10,87290,8749
1,20,89250,8944
1,30,90990,9115
1,40,92510,9265
1,50,93820,9394
1,60,94950,9505
1,70,95910,9599
1,80,96710,9678
1,90,97380,9744
2,00,97930,9798
2,10,98380,9842
2,20,98750,9878
2,30,99040,9906
2,40,99270,9929
2,50,99450,9946
2,60,99590,9960
2,70,99690,9970
2,80,99770,9978
2,90,99840,9984
3,00,99880,9989
3,10,99920,9992
3,20,99940,9994
3,30,99960,9996
3,40,99970,9997
3,50,99980,9998
kk67
−3,50,00020,0002
−3,40,00030,0003
−3,30,00040,0004
−3,20,00060,0005
−3,10,00080,0008
−3,00,00110,0011
−2,90,00150,0015
−2,80,00210,0021
−2,70,00290,0028
−2,60,00390,0038
−2,50,00520,0051
−2,40,00690,0068
−2,30,00910,0089
−2,20,01190,0116
−2,10,01540,0150
−2,00,01970,0192
−1,90,02500,0244
−1,80,03140,0307
−1,70,03920,0384
−1,60,04850,0475
−1,50,05940,0582
−1,40,07210,0708
−1,30,08690,0853
−1,20,10380,1020
−1,10,12300,1210
−1,00,14460,1423
−0,90,16850,1660
−0,80,19490,1922
−0,70,22360,2206
−0,60,25460,2514
−0,50,28770,2843
−0,40,32280,3192
−0,30,35940,3557
−0,20,39740,3936
−0,10,43640,4325
−0,00,47610,4721
kk67
0,00,52390,5279
0,10,56360,5675
0,20,60260,6064
0,30,64060,6443
0,40,67720,6808
0,50,71230,7157
0,60,74540,7486
0,70,77640,7794
0,80,80510,8078
0,90,83150,8340
1,00,85540,8577
1,10,87700,8790
1,20,89620,8980
1,30,91310,9147
1,40,92790,9292
1,50,94060,9418
1,60,95150,9525
1,70,96080,9616
1,80,96860,9693
1,90,97500,9756
2,00,98030,9808
2,10,98460,9850
2,20,98810,9884
2,30,99090,9911
2,40,99310,9932
2,50,99480,9949
2,60,99610,9962
2,70,99710,9972
2,80,99790,9979
2,90,99850,9985
3,00,99890,9989
3,10,99920,9992
3,20,99940,9995
3,30,99960,9996
3,40,99970,9997
3,50,99980,9998
kk89
−3,50,00020,0002
−3,40,00030,0002
−3,30,00040,0003
−3,20,00050,0005
−3,10,00070,0007
−3,00,00100,0010
−2,90,00140,0014
−2,80,00200,0019
−2,70,00270,0026
−2,60,00370,0036
−2,50,00490,0048
−2,40,00660,0064
−2,30,00870,0084
−2,20,01130,0110
−2,10,01460,0143
−2,00,01880,0183
−1,90,02390,0233
−1,80,03010,0294
−1,70,03750,0367
−1,60,04650,0455
−1,50,05710,0559
−1,40,06940,0681
−1,30,08380,0823
−1,20,10030,0985
−1,10,11900,1170
−1,00,14010,1379
−0,90,16350,1611
−0,80,18940,1867
−0,70,21770,2148
−0,60,24830,2451
−0,50,28100,2776
−0,40,31560,3121
−0,30,35200,3483
−0,20,38970,3859
−0,10,42860,4247
−0,00,46810,4641
kk89
0,00,53190,5359
0,10,57140,5753
0,20,61030,6141
0,30,64800,6517
0,40,68440,6879
0,50,71900,7224
0,60,75170,7549
0,70,78230,7852
0,80,81060,8133
0,90,83650,8389
1,00,85990,8621
1,10,88100,8830
1,20,89970,9015
1,30,91620,9177
1,40,93060,9319
1,50,94290,9441
1,60,95350,9545
1,70,96250,9633
1,80,96990,9706
1,90,97610,9767
2,00,98120,9817
2,10,98540,9857
2,20,98870,9890
2,30,99130,9916
2,40,99340,9936
2,50,99510,9952
2,60,99630,9964
2,70,99730,9974
2,80,99800,9981
2,90,99860,9986
3,00,99900,9990
3,10,99930,9993
3,20,99950,9995
3,30,99960,9997
3,40,99970,9998
3,50,99980,9998