Page 32 - TUTORIAL MATEMATIKA IPA KELAS XI-2

TURUNAN FUNGSI ALJABAR

2
2
58. + = 75 → = 75 −
2
3
= = (75 − ) = 75 −
′
2
2
→ = 75 − 3 = 3(25 − ) = 3(5 − )(5 + )
′
∴ = 0 → = −5 , = 5

------------- ++++++++++ -------------
-5 5
Mencapai maksimum pada = 5 → = 50 → = 50.5 = 250

59. = 36

2
′
2
3
= → = 3 → = 3

2
→ . = 3

2
→ 36 . = 3

1 2
→ =
12
12
→ = … ( )
2
2
2
2
= 6 → 24 = 6 → = 4 … ( )
12
Dari (i) dan (ii) : = = 3
4

2
60. = .
2
2
2
= 2 + 4 → 96 = 2 + 4 → 48 = + 2 → = 48− 2
2
2
1
3
2
2
= . = . 48− = 24 −
2 2
3
3
3
2
′
2
2
2
= 24 − → 0 = 24 − → = 24 → = 16 → = 4 (sisi tidak boleh -)
2 2 2
48−4 2 32 2 3
= 4 → = = = 4 → = 4 . 4 = 64
2.4 8

61.
B

O A
Persamaan garis g: + =
∴ (4, 3) → 4 + 3 =
4
→ 4 = − 3 → 4 = ( − 3) → =
−3
1 1 1 4 2 2
→ = = = . =
2 2 2 2 −3 −3
2
′
′
2
→ = 4 ( −3)−2 .1 = 2 −12 ; = 0 → 2 − 12 = 0
( −3) 2 ( −3) 2
2 ( − 6) = 0 → = 0 , = 6 karena sisi harus > 0 maka nilai B yang memenuhi adalah 6
4.6
̅̅̅̅
2
2
2
2
→ = = 8 → = √ + = √8 + 6 = 10
6−3
‘LEARNING IS FUN’ 31