Apps. and Interpretation for IBDP Maths Ebook 1 | Page 201

55
Paper 1 – Parallel Tangents
Example
Consider the function
f x
2
( ) 4x
3
� � and g( x) �2x
� 5.
(a) Find the expression of f� ( x)
.
(b) Write down the expression of g� ( x)
.
(c) Find the value of x such that the gradients of f( x ) and gx ( ) are the same.
(d) Write down the value of f( x ) when the gradients of f( x ) and gx ( ) are the
same.
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Solution
(a) f �( x) �4(2 x) � 0
(A1) for correct derivatives
f �( x) � 8x
A1 N2
(b) g�( x) � 2
A1 N1
(c) f �( x) � g�( x)
(d)
Exercise 55
8x � 2
(M1) for setting equation
1
x � A1 N2
4
13
4
A1
N1
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1. Consider the function
2
f ( x) 2x x
� � and
g( x)
2
� .
x
(a) Find the expression of f� ( x)
.
(b) Write down the expression of g� ( x)
.
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