Page 50 - Hybrid PBD 2022 Tg 5 - Matematik Tambahan

Matematik Tambahan Tingkatan 5 Bab 2 Pembezaan

(b) Diberi f(x) = ax + bx + 3, cari nilai a dan b jika (c) Diberi y = 3x – 6x , cari julat x jika d y , 0 dan
3
3
2
f‘(2) = 14 dan f”(–1) = –6. d y dx
2
Given f(x) = ax + bx + 3, find the values of a and b if 2 . 0.
3
f‘(2) = 14 and f“(–1) = –6. dx d y
Given that y = 3x – 6x , find the range of x if , 0 and
3
2
d y dx
2
Diberi/Given f(x) = ax + bx + 3 dx 2 . 0.
3
f’(x) = 3ax +b Diberi/Given y = 3x – 6x 2
2
3
f"(x) = 6ax d y = 9x –12x
2
f“(–1) = 6a(–1) = –6 dx 9x – 12x , 0
2
a = 1 3x(3x – 4) , 0
f’(2) = 12 + b = 14 4
b = 2 0 , x , 3
2
d y
Apabila/When . 0
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dx 2
18x – 12 . 0
x . 2
3
Maka, julat x ialah/Hence, the range of x is
2 , x , 4
3 3
Kriteria Kejayaan: ............................................................................................ .
Saya berjaya
• Mencari terbitan kedua bagi fungsi terhadap x.
• Menghubungkait dan membezakan terbitan pertama dan terbitan kedua.
PBD
PBD 2.4 Aplikasi Pembezaan Buku Teks
PBD
Application of Differentiation ms. 51 – 79
17. Cari fungsi kecerunan bagi setiap lengkung yang diberi dan seterusnya cari Aplikasi Pembezaan
kecerunan tangen pada titik x yang diberi. SP 2.4.1 TP3 Application of
Find the gradient function for each of the given curves and then find the gradient of the tangent at the Differentiation
given value of x. NOTA

x
1
3
y = x – x pada/at x = 2. (a) y = (5 – 3x) pada/at x = –1 , x ≠ 5
3

2 2
Fungsi kecerunan, d y = 3x – 1 Fungsi kecerunan/Gradient function,
The gradient function dx 2 d y = (5 – 3x) – x(–3)
Kecerunan tangen di x = 2 dx (5 – 3x) 2
Gradient of the tangent at x = 2 Kecerunan tangen di x = –1
= 3(2) 2 – 1 Gradient of the tangent at x = –1
2 (5 – 3(–1)) – (–1)(–3)
= 5 =
(5 – 3(–1)) 2
8 – 3
=
8 2
5
=
64

6
(b) f(x) = x – + 3 pada/at x = –2. (c) f(x) = x – 1 pada/at x = 5.
2
x d y 1
d y 6 Fungsi kecerunan/Gradient function =
x – 1
Fungsi kecerunan/Gradient function = 2x + dx 2
dx x 2 Kecerunan tangen di x = 5
Kecerunan tangen di x = –2 Gradient of the tangent at x = 5
Gradient of the tangent at x = –2 1
6 = 2
5 – 1
= 2(–2) +
(–2) 2 1
6 5 =
= –4 + = – 4
4 2
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