Page 29 - TUTORIAL_MAT_IPS_K11-2

TURUNAN FUNGSI ALJABAR

0
2
′
42. = tan 45 = 1 ; = + 5 − 24 → = 2 + 5
∴ = 1 → 1 = 2 + 5 → = −2
2
∴ = −2 → = (−2) + 5. (−2) − 24 = −30 → (−2, −30) {titik singgung}
PGS: − (−30) = 1( − (−2)) → + 30 = + 2 → = − 28

43. ∴ Menentukan titik potong kurva dan garis :
2
− 2 − 3 = 2 + 9
2
→ − 4 − 12 = 0
→ ( − 6)( + 2) = 0 → = 6, = −2

′
∴ Persamaan gradien kurva: = 2 − 2

2
∴ = 6 → = 6 − 2.6 − 3 = 21 → (6, 21) {titik singgung}
(6) = 2.6 − 2 = 10
PGS1: − 21 = 10( − 6) → = 10 − 39

2
∴ = −2 → = (−2) − 2. (−2) − 3 = 5 → (−2, 5) {titik singgung}
(−2) = 2. (−2) − 2 = −6
PGS2: − 5 = −6( − (−2)) → = −6 − 7

1
2
2
3
44. = − 2 − 12 + 5 → m = ′ = − 4 − 12.
3
∴ Garis singgung mendatar terjadi jika gradien = 0
2
∴ = 0 → 0 = − 4 − 12
→ ( − 6)( + 2) = 0 → = −2 , = 6
1 3 2 55 55
∴ = −2 → = . (−2) − 2. (−2) − 12. (−2) + 5 = → (−2, )
3 3 3
1
2
3
∴ = 6 → = . (6) − 2. (6) − 12. (6) + 5 = −67 → (6, −67)
3

2
5 0.( +6)−5.2 −10
′
45. = → = =
2
2
2
+6 ( +6) 2 ( +6) 2
Gradien terkecil adalah 0 pada saat x = 0.
5 5 5
∴ = 0 → = = → (0, )
2
0 +6 6 6
5 5
PGS: − = 0( − 0) → =
6 6

1
46. Garis singgung pada kurva tegak lurus garis = − + 2, berarti gradien garis singgung =
3
1
− −1 ⁄ 3 = 3.
2
3
2
= − → = ′ = 3 − 2
2
∴ = 1 → (1) = 3. 1 − 2 . 1 = 3 − 2
∴ (1) = 3 → 3 − 2 = 3 → = 0
2
3
2
3
∴ = 1 → = = − = 1 − 0. 1 = 1 → (1, 1) {titik singgung}
PGS: − 1 = 3( − 1) → = 3 − 2
‘LEARNING IS FUN’ 28