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Bài tập CALCULUS 23
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Created by T. Madas
Question 88
(***+)
r
h
The figure above shows a closed cylindrical can of radius r cm and height h cm .
a) Given that the surface area of the can is 192π cm 2 , show that the volume of the
can, V cm3 , is given by
V = 96π r − π r 3 .
b) Find the value of r for which V is stationary.
c) Justify that the value of r found in part (b) gives the maximum value for V .
d) Calculate the maximum value of V .
MP1-K , r = 4 2 ≈ 5.66 , Vmax = 256π 2 ≈ 1137
Created by T. Madas
Created by T. Madas
Question 89
(***+)
The curve C has equation
y = 2 x3 − 9 x 2 + 12 x − 10 .
a) Find the coordinates of the two points on the curve where the gradient is zero.
The point P lies on C and its x coordinate is −1 .
b) Determine the gradient of C at the point P .
The point Q lies on C so the gradient at Q is the same as the gradient at P .
c) Find the coordinates of Q .
C1G , (1, −5 ) , ( 2, −6 ) , 36 , Q ( 4, 22 )
Created by T. Madas
Created by T. Madas
Question 90
(***+)
The gradient function at every point on a curve C is given by
dy
= ( kx − 3) x ,
dx
where k is a non zero constant.
The point P ( 4, 40 ) lies on C and the gradient at P is 34 .
Determine an equation of C .
5
3
C1V , y = 2 x 2 − 2 x 2 − 8
Created by T. Madas
