Apps. and Interpretation for IBDP Maths Ebook 1 | Page 204

Your Practice Set – Applications and Interpretation for IBDP Mathematics
2. Let
f x � �x � x � x � x � .
4 3 2
( ) 20 142 420 600
(a) Find the expression of f� ( x)
.
(b) Find the intervals of x such that f( x ) is increasing.
[3]
[3]
3. The table below shows the behaviour of f( x ) and f� ( x)
:
x � 3 x � 3 3 �x
� 11 x � 11 x � 11
f( x )
5 2
f� ( x)
Positive Zero Negative Zero Positive
(a) (i) Write down the equation of the tangent at x � 3.
(ii) Write down the equation of the tangent at x � 11.
(b) Write down the intervals when f( x ) is increasing.
(c) Write down the coordinates of the minimum point of f( x ).
(d) State which functional value is smaller: f (5) or f (9) .
[2]
[2]
[2]
[1]
4. The table below shows the behaviour of f( x ) and f� ( x)
:
x �� 4 x �� 4 �4� x � 1 x � 1 1�x
� 5 x � 5 x � 5
f( x )
0 20 12
f� ( x)
Negative Zero Positive Zero Negative Zero Negative
(a) (i) Write down the equation of the tangent at x �� 4.
(ii) Write down the equation of the tangent at x � 5.
(b) Write down the intervals when f( x ) is decreasing.
(c) Write down the coordinates of the maximum point of f( x ).
(d) State which functional value is the largest: f (2) , f (5) or f (8) .
[2]
[2]
[2]
[1]
194
SE Production Limited