Apps. and Interpretation for IBDP Maths Ebook 1 | Page 200

Your Practice Set – Applications and Interpretation for IBDP Mathematics
4
2. Let f ( x) �3x
� . The line L is the normal to the curve of f at (1, � 1) .
2
x
(a) Find the expression of f� ( x)
.
(b) Find the gradient of L .
(c) Find the equation of L in the form y �ax � b .
[2]
[2]
[2]
3. Let
3 2
f ( x) � ax � 2x
� 1. The line L is the tangent to the curve of f at (3, 27a � 17) .
(a) Find the expression of f� ( x)
in terms of a .
(b) The gradient of L is 96. Find the value of a .
(c) Find the equation of L in the form y �mx � c .
[2]
[2]
[2]
4. Let
f ( x) 3
3
� � ax . The line L is the normal to the curve of f at (2, 3 8 a)
� .
(a) Find the expression of f� ( x)
in terms of a .
(b) Find the gradient of L in terms of a .
(c)
Write down the value of a if the gradient of L is
(d) Find the equation of L in the form y �mx � c .
1
� .
12
[2]
[2]
[1]
[2]
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