Page 20 - Modul A+1 Matematik Tambahan Tingkatan 5

2.3 Pembezaan Peringkat Kedua Buku Teks
The Second Derivative m.s. 49-50

dy d y
2
1. Cari dan bagi setiap yang berikut.
dx dx 2
dy d y
2
Find and for each of the following. TP 2
dx dx 2
Contoh/Example Tip SPM
y = 4x + 2x – 5 d y d dy
3
2
x • = ( )
y = 4x + 2x – 5x –1 dx 2 dx dx
3
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d
BAB 2 dy = 12x + 2 + 5x d y 2 = 24x – 10x –3 • f(x) = (f(x))
2
–2
2
dx
dx
dx
2
5
dy 2
≠
= 12x + 2 + = 24x – 10 • d y 2 ( )
2
x 2 x 3 dx dx
(a) y = (1 – 2x ) (b) y = 2x – 5
2 4
3
dy 2 3 x
dx = 4(1 – 2x ) (– 4x) y = 2x – 5x –1
3
= –16x(1 – 2x ) dy 2 5
2 3
d y 2 2 2 3 dx = 6x + x 2
2
2
dx 2 = –16x(3)(1 – 2x ) (– 4x) + (1 – 2x ) (–16) = 6x + 5x –2
= (1 – 2x ) (192x + 32x – 16) = 6x + 5
2 2
2
2
2
= (1 – 2x ) (224x – 16) x 2
2
2 2
d y = 12x – 10
2
dx 2 x 3
2. Selesaikan masalah berikut.
Solve the following problems. TP 3
Contoh/Example (a) Diberi bahawa f(x) = (5x – 2) , cari f '(1) dan f ʺ(0).
5
Given that f(x) = (5x – 2) , find f '(1) and f ʺ(0).
5
Diberi g(x) = 3x + 2x – 9x – 7, cari gʹ(4) dan gʺ(–1).
2
3
Given g(x) = 3x + 2x – 9x – 7, find gʹ(4) and gʺ(–1). f(x) = (5x – 2) 5
3
2
f ʹ(x) = 5(5x – 2) (5)
4
g(x) = 3x + 2x – 9x – 7 = 25(5x – 2) 4
3
2
gʹ(x) = 9x + 4x – 9 f ʹ(1) = 25(5(1) – 2) 4
2
gʹ(4) = 9(4) + 4(4) – 9 = 2 025
2
= 151 f ʺ(x) = 25(4)(5x – 2) (5)
3
gʺ(x) = 18x + 4 = 500(5x – 2) 3
gʺ(–1) = 18(–1) + 4 f ʺ(0) = 500(5(0) – 2) 3
= –14 = – 4 000

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