Page 28 - TUTORIAL MATEMATIKA IPS KELAS XI-2

TURUNAN FUNGSI ALJABAR

39. = −1
2
→ −1 = − + 3 + 9
2
→ − 3 − 10 = 0
→ ( − 5)( + 2) = 0 → = 5 , = −2
∴ = −2 → (−2, −1)
∴ = 5 → (5, −1)

′
2
= − + 3 + 9 → = −2 + 3

PGS1, melalui titik singgung (-2, -1)
→ (−2) = −2. −2 + 3 = 7
∴ − = ( − )
1
1
→ − (−1) = 7( − (−2))
→ + 1 = 7( + 2)
→ = 7 + 13

PGS2, melalui titik singgung (5, -1)
→ (5) = −2.5 + 3 = −7
∴ − = ( − )
1
1
→ − (−1) = −7( − 5)
→ + 1 = −7( − 5)
→ = −7 + 34

40. Garis singgung sejajar dengan garis K: 4 − 2 + 3 = 0 maka gradien garis singgung = gradien
4
garis K = − = − = 2.
−2
2
′
= 3 − − 4 → = = 6 − 1
1
∴ = 2 → 2 = 6 − 1 → =
2
1 1 2 1 15 1 15
∴ = → = 3. ( ) − − 4 = − → ( , − ) {titik singgung}
2 2 2 4 2 4
15 1 15 19
PGS : − (− ) = 2 ( − ) → + = 2 − 1 → = 2 −
4 2 4 4

41. Garis singgung tegak lurus dengan garis L: 3 + 6 − 7 = 0 maka gradien garis singgung =
−1 −1 6
= = = 2.
−3 ⁄ 6 3
′
2
= −5 − 3 + 2 → = = −10 − 3
1
∴ = 2 → 2 = −10 − 3 → = −
2
1 1 2 1 9 1 9
∴ = − → = −5. (− ) − 3. (− ) + 2 = → (− , ) {titik singgung}
2 2 2 4 2 4
9 1 9 13
PGS: − ( ) = 2 ( − (− )) → − = 2 + 1 → = 2 +
4 2 4 4

‘LEARNING IS FUN’ 27