Page 153 - ADVANCED MATH F.5

Form Five Form Five

′
2. (a) ( ) 5;fx = f ′ (1) 5= (d) f ′ ( )x = 2 ;xf ′ (3) 6=
(b) f ′ ( ) 3x = x − 2 2 ;xf ′ (2) 8
=
′
(c) ( )1;fx ′ = f ′ (2)1= (e) fx 2x − 3 ; f ′ (4) = − 1
( ) = −
FOR ONLINE READING ONLY
32
3. f ′ ( )5 4 ;x xf ′= − (3) = − 7; f ′ ( 1)9− =

dy dy
4. (a) y = 1080; = 540 (c) y = 1; = − 1
dx dx
dy
(b) y = 2; = 9
dx

Differentiation of a function

Teaching steps
1. Guide students through discussion to explore differentiation of
function as a process of finding the derivative of a function or
rate of change of one variable with respect to another variable.

2. Instruct students through discussion to recognize a differentiable
function at a given point. Assist students to identify functions
that cannot be differentiated.

Derivatives of polynomial functions
Teaching steps
1. Guide students through discussion to deduce the power rule
n
for differentiating the polynomial function ()fx = x from first
principles.

2. Assist students through discussion to obtain the power rule
d
n
x
formula as ( ) = f ′ () x = nx n− 1 . Allow students to share
dx
alternative methods of deducing the power rule.

147
Mathematics for Advanced Secondary Schools

ADVANCED MATH F.5 TG CHAPTERS.indd 147 30/06/2024 18:02:36
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ADVANCED MATH F.5 TG CHAPTERS.indd 147