Apps. and Interpretation for IBDP Maths Ebook 1 | Page 203

56
Paper 1 – Increasing and Decreasing Functions
Example
Let
3
f ( x) � x � 48x
� 102 .
(a) Write down the y -intercept of f( x ).
(b) Find the expression of f� ( x)
.
(c) Find the intervals of x such that f( x ) is increasing.
[1]
[2]
[3]
15
Solution
(a) 102 A1 N1
(b)
f � x � x � � (A1) for correct derivatives
2
( ) 3 48(1) 0
f � x � x � A1 N2
2
( ) 3 48
(c) f�( x) � 0
2
3x �48 � 0
(A1) for correct inequality
By considering the graph of
y� � ,
2
3x
48
x �� 4 or x � 4 . A2 N3
[1]
[2]
[3]
Exercise 56
1. Let
3 2
f ( x) � 2x �33x �108x
� 125 .
(a) Find the expression of f� ( x)
.
(b) Find the interval of x such that f( x ) is decreasing.
[3]
[3]
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