Apps. and Interpretation for IBDP Maths Ebook 1 | Page 208

Your Practice Set – Applications and Interpretation for IBDP Mathematics
(d) 3�x
� 6
A2 N2
(e) (i) 155 A1 N1
[2]
(ii)
2
f �(4) � 6(4) �54(4) � 108
(M1) for substitution
f �(4) �� 12
A1 N2
(iii)
The equation of tangent:
y�155 � �12( x� 4)
(M1) for substitution
y�155 � �12x�
48
12x� y� 203 � 0
A1 N2
[5]
Exercise 58
1. Let
3 2
f ( x) � �x �3x � 24x
� 1. The graph of f has a local minimum at ( � 2, r)
.
(a) Find the value of r .
(b) Find f� ( x)
.
(c) Find the coordinates of the local maximum point of the graph of f .
(d) Write down the intervals of x when f( x ) is decreasing.
(e) (i) Write down the value of f (0) .
[2]
[2]
[3]
[2]
(ii) Find the value of f � (0) .
(iii) Hence, find the equation of tangent at x � 0 , giving the answer in general
form.
(iv)
Find the x -intercept of the tangent.
[7]
2. Let
3
f ( x) � 2x �150x
� 150 . The graph of f has a local maximum at ( r , 350) .
(a) Find the value of r .
(b) Find f� ( x)
.
[2]
[2]
198
SE Production Limited