Analysis and Approaches for IBDP Maths Ebook 2 | Page 152

Your Practice Set – Analysis and Approaches for IBDP Mathematics
4. The function f is defined by
f( x)
�
x
x
2
2
� 25
� 25
, x �� 5, x � 5 .
(a) Write down the equations of the vertical asymptotes of f( x ).
(b) Find f� ( x)
.
(c) Show that there is no local minimum of f( x ).
(d) Find f�� ( x)
.
(e) Show that there is no point of inflexion of f( x ).
A B
It is given that f ( x)
� C
x�5 � x�5
� , where A , B and C are constants.
[2]
[2]
[3]
[3]
[2]
(f) (i) Find the values of A , B and C .
(ii) Hence, write down the equation of the horizontal asymptote of f( x ).
[7]
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