Apps. and Interpretation for IBDP Maths Ebook 1 | Page 198

Your Practice Set – Applications and Interpretation for IBDP Mathematics
2. Consider the function
f x
2
( ) 4x
6
� � .
(a) Find the expression of f� ( x)
.
(b) Find the gradient of the graph of f( x ) at
1
x � .
4
[2]
(c) The normal to f( x ) at x� a has gradient 1
16 . Find the value of a . [3]
[2]
3. Consider the function
f ( x)
1 1
x
2 x
2
� � .
(a) Find the value of f ( � 2) .
(b) Find the expression of f� ( x)
.
(c) The normal to f( x ) at x
of a .
� a has gradient
9
� , where a � 1. Find the value
28
[2]
[2]
[4]
4. Consider the function
3
x
f ( x)
� � x , where a is a positive constant.
a
(a)
Write down the value of the y -intercept.
(b) Find the expression of f� ( x)
in terms of a .
(c) The normal to f( x ) at x � 2 has gradient
1
� . Find the value of a .
3
[1]
[2]
[3]
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