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Bài tập CALCULUS 26
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Created by T. Madas
Question 99
(***+)
y = − x2 + 8x − 2
y
y = x 2 − 10 x + 26
A
B
R
O
x
The figure above shows the graphs of the curves with equations
y = − x 2 + 8 x − 2 and
y = x 2 − 10 x + 26 .
The two curves intersect each other at the points A and B .
The finite region R bounded by the two curves is shown shaded in the figure above.
Show that the area of R is exactly 125 .
3
C2L , proof
Created by T. Madas
Created by T. Madas
Question 100
(***+)
25x
15x
y
20x
The figure above shows a solid triangular prism with a total surface area of 3600 cm 2 .
The triangular faces of the prism are right angled with a base of 20x cm and a height
of 15x cm . The length of the prism is y cm .
a) Show that the volume of the prism, V cm3 , is given by
V = 9000 x − 750 x3 .
b) Find the value of x for which V is stationary.
c) Show that the value of x found in part (b) gives the maximum value for V .
d) Determine the value of y when V is maximum.
C2D , x = 2 , y = 20
Created by T. Madas
Created by T. Madas
Question 101
(***+)
The curve C has equation
y = ax −
b
x2
, x ≠ 0,
where a and b are non zero constants.
The gradient of C at the points where x = 1 and x = −2 is 14 and 5 , respectively.
Find the value of a and the value of b .
a = 6, b = 4
Question 102
(***+)
f ′( x) = 5 −
8
x2
, x ≠ 0.
Find the value of f ( 4 ) , given that 2 f (1) = 4 + f ( 2 ) .
C1X , f ( 4 ) = 14
Created by T. Madas
