Page 30 - TUTORIAL MATEMATIKA IPA KELAS XI-2

TURUNAN FUNGSI ALJABAR

′
2
47. = 2 + + → = 4 +
′
PGS : = 8 + 2 → = = 8
∴ = 8, = 1 → 8 = 4.1 + → = 4
∴ = 1 → = 8.1 + 2 = 10
2
∴ = 10 → 10 = 2. 1 + . 1 + = 2 + + → 8 = + = 4 + → = 4
. = 4.4 = 16

2
48. ∴ ( , ) → = − + 6 − 8
→ ( ) = −2 + 6 ; ( ) = 2 − 1 = −1
2 − 1 −2
−1
→ −2 + 6 =
−2
→ (−2 + 6)( − 2) = − 1
2
2
→ −2 + 10 − 12 = − + 6 − 8 − 1
2
→ 0 = − 4 + 3
→ ( − 3)( − 1) = 0 → = 3, = 1
2
∴ = 3 → = −3 + 6.3 − 8 = 1, memenuhi.
2
∴ = 1 → = −1 + 6.1 − 8 = −3 tidak memenuhi karena q harus bilangan bulat +.
+ = 3 + 1 = 4

2
49. ∴ ( , ) → = − ( + 1) + 6 … ( )
∴ = 2 + 3 → = 2
∴ = 2 + 3 → = 2 + 3 … ( )
′
= = 2 − ( + 1)
3+
∴ = 2 → 2 = 2 − − 1 → = … ( )
2
2
2
Dari (i) dan (ii) → − ( + 1) + 6 = 2 + 3 → − − − 2 + 3 = 0 … ( )
3+ 2 3+ 3+ 3+
Dari (iii) dan (iv) → ( ) − ( ) − ( ) − 2 ( ) + 3 = 0
2 2 2 2
2
2
9+6 + 2 3 + 2 3+ 6+2 9+6 + −6 −2 −6−2 −12−4 +12
→ − − − + 3 = = 0
4 2 2 2 4
2
− +6 −9
2
2
→ = 0 → − 6 + 9 = 0 → ( − 3) = 0 → = 3
2
3+3
Dari (iii) didapat = = 1
2.3
Dari (ii) didapat = 2.1 + 3 = 5

′
50. ( ) = 1 − 3
2√2 −3
′
∴ ( ) = 0 → 1 − 3 = 0 → 1 = 3 → 2√2 − 3 = 3 → 4(2 − 3 ) = 9
2√2 −3 2√2 −3
8 −9
→ 8 − 12 = 9 → =
12
5 5 8 −9 8 −9 8 −9 24 −24 +27 8 −9 3
∴ = → = + √2 − 3 = + √ = +
4 4 12 12 12 12 12 4
2 8 −9
→ = → 24 = 32 − 36
4 12
60 15
→ 60 = 32 → = =
32 8

‘LEARNING IS FUN’ 29