- Trang chủ >>
- Đề thi >>
- Đề thi lớp 1
Bài tập CALCULUS 10
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (924.51 KB, 3 trang )
Created by T. Madas
Question 38
(**+)
y
y = x2 − 5 x + 9
A
y =5
B
O
x
The figure above shows a quadratic curve and a straight line with respective equations
y = x2 − 5 x + 9
and
y = 5.
The points A and B are the points of intersection between the straight line and the
quadratic curve.
a) Find the coordinates of A and B .
b) Calculate the exact area of the finite region bounded by the quadratic curve and
the straight line, shown shaded in the above figure.
MP1-R , A (1,5 ) , B ( 4,5 ) , area = 9
2
Created by T. Madas
Created by T. Madas
Question 39
(**+)
The curve C with equation y = f ( x ) has gradient function
dy
7
= 9 x2 + 2 , x ≠ 0 .
dx
x
The point A ( −1, −1) lies on C .
Find an equation for C .
y = 3 x3 −
Question 40
7
−5
x
(**+)
y = 2x +
8
x2
, x ≠ 0.
Find the coordinates of the stationary point of y and determine its nature.
C2A , min ( 2,6 )
Created by T. Madas
Created by T. Madas
Question 41
(***)
24cm
x
64 cm
x
x
figure 2
figure 1
An open box is to be made out of a rectangular piece of card measuring 64 cm by
24 cm . Figure 1 shows how a square of side length x cm is to be cut out of each
corner so that the box can be made by folding, as shown in figure 2 .
a) Show that the volume of the box, V cm3 , is given by
V = 4 x3 − 176 x 2 + 1536 x .
b) Show further that the stationary points of V occur when
3 x 2 − 88 x + 384 = 0 .
c) Find the value of x for which V is stationary.
(You may find the fact 24 ×16 = 384 useful.)
d) Find, to the nearest cm3 , the maximum value for V , justifying that it is indeed
the maximum value.
x = 16 , Vmax ≈ 3793
3
Created by T. Madas
