Page 35 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Differentiation

Example 16
1
Given that y = 3x + , and x changes from 2 to 1.98, find
x
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(a) the approximate change in y,
(b) the approximate value of y.
Solution
1 1
(a) y = 3x + x (b) When x = 2, y = 3(2) + 2
= 3x + x –1 = 13
dy 2
= 3 – x –2
dx dy 1
When x = 2 and δx = 1.98 – 2 When x = 2, dx = 3 – 2 2
= –0.02 = 2.75
δy  dy × δx f(x + δx)  y + dy δx
dx
dx

δy = 3 – x 1 2 × (–0.02) = 13 + 2.75(–0.02)
2

= 3 – 2 1 2 × (–0.02) = 6.445
= 2.75(–0.02)
= –0.055

Mastery

1. The diagram below shows a plate which Solution
is made up of a rectangle ABCD and
semicircles at both ends. The area of the (a) Let y = diameter of the semicircle
rectangle is 200 cm . Perimeter of the plate,
2
P = 2x + 2πr
A B
= 2x + πy
Area of ABCD = 200
xy = 200
Form 5 D x cm C y = 200
x

(a) Show that the perimeter, P of the Hence, P = 2x + πy 200
plate is P = 2x + 200π . = 2x + π  x 
x
(b) Find the minimum perimeter P and = 2x + 200π
the corresponding value of x. x
(b) P = 2x + 200πx –1
dP 200π
= 2 –
dx x 2
188

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