Page 31 - TUTORIAL MATEMATIKA IPA KELAS XI-2

TURUNAN FUNGSI ALJABAR

2
′
51. ( ) = ( ) = − + 6 − 5
2
′
∴ ( ) = 0 → 0 = − + 6 − 5
→ (− + 5)( − 1) = 0 → = 5, = 1

--------------- +++++++ ---------------
1 5
Kecepatan mencapai maksimum pada saat t = 5s.

1 1 3
2
2
52. Untung = = (50 − ) − ( + 35 + 25) = − + 15 − 25
2 4 4
3
′
→ = − + 15
2
3
3
′
∴ = 0 → 0 = − + 15 → = 15 → = 10
2 2
3
2
= − . 10 + 15.20 − 25 = 200
4

2
2
53. Laba = = 40 − (75 + 2 + 0,1 ) = −0,1 + 38 − 75
′
→ = −0,2 + 38
∴ ′ = 0 → 0 = −0,2 + 38 → 38 = 0,2 → = 190
2
= −0,1. 190 + 38.190 − 75 = 3535

120
′
2
54. = (3 − 900 + ) = 3 − 900 + 120 → = 6 − 900

′
∴ = 0 → 6 − 900 = 0 → 6 = 900 → = 150

3
2
( −2.000 +3.000.000 )
2
55. / = = = − 2.000 + 3.000.000

′
→ = 2 − 2.000
′
∴ = 0 → 2 − 2.000 = 0 → = 1000

20.000 2
56. Biaya = = (390 − − ) = 390 − 20.000 −

Jual = = 150
2
2
Untung = = 150 − (390 − 20.000 − ) = −240 + 20000 +
′
→ = −240 + 2
′
∴ = 0 → −240 + 2 = 0 → 240 = 2 → = 120
2
= −240.120 + 20.000 + 120 = 5600 = 5.600.000

57. + = 8 → = 8 −
3
2
4
2
2
2
2
= . = (8 − ) . = 64 − 16 +
2
′
3
2
→ = 128 − 48 + 4 = 4 (32 − 12 + ) = 4 (8 − )(4 − )
∴ ′ = 0 → = 0, = 8, = 4

------------- +++++ --------- +++++++
0 4 8
Mencapai maksimum pada = 4 → = 8 − 4 = 4 → ℎ = 4 − 4 = 0
‘LEARNING IS FUN’ 30