Analysis and Approaches for IBDP Maths Ebook 1 | Page 154

Your Practice Set – Analysis and Approaches for IBDP Mathematics
51
Paper 1 Section A – Patterns of the -th derivative
Example
Let f( x) � e ax .
(a) Write down f� ( x)
, f�� ( x)
and
(b)
Find an expression for
f (3) ( x ) in terms of a .
( n
f ) ( x ) in terms of a .
[3]
[2]
Solution
(a)
ax
f �( x)
� ae
A1 N1
2 ax
f ��( x)
� a e
A1 N1
(3) 3 ax
f ( x)
a e
� A1 N1
( n
(b)
) n ax
f ( x)
� a e
A2 N2
[3]
[2]
Exercise 51
1. Let
f x
�5
( ) e x
� .
(a) Write down f� ( x)
, f�� ( x)
and
(b)
Find an expression for
( n
f ) ( x ).
f (3) ( x ).
[3]
[2]
2. Let f ( x) �� sin x .
(a) Write down f� ( x)
, f�� ( x)
,
(b)
Find an expression for
f
(3) ( x ) and
(2 n
f ) ( x ).
f (4) ( x ).
[2]
[3]
146
SE Production Limited