Analysis and Approaches for IBDP Maths Ebook 1 | Seite 175

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Exercise 58
1. Consider
3 2
f ( x) x 6x 15x
� � � .
(a) Find the values of f ( � 5) and f (0) .
[3]
(b) Find the set of values of x for which f is decreasing.
[4]
(c) Show that the coordinates of the point of inflexion on the graph of f are ( � 2, 46)
for x �� 5.
[6]
It is given that the minimum point on the graph of f are (1, � 8) .
14
(d) Sketch the graph of f , for x �� 5.
[3]
2. Consider
f ( x) 1 9x 3x x
2 3
� � � � .
(a) Find the values of f (0) and f (3) .
[3]
(b) Find the set of values of x for which f is increasing.
[4]
(c) Show that the coordinates of the point of inflexion on the graph of f are (1,12)
for x � 3.
[6]
It is given that the minimum point on the graph of f are ( �1, � 4) .
(d) Sketch the graph of f , for x � 3.
[3]
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