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Bài tập CALCULUS 66
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Created by T. Madas
Question 228
(****)
f ( x) =
4 − 6x
x2
, x ≠ 0.
a) Find the coordinates of the stationary point of f ( x ) and determine its nature.
b) Show clearly that f ( x ) has a point of inflection and determine its coordinates.
(
)
min 4 , − 9 ,
3 4
Created by T. Madas
( 2, −2 )
Created by T. Madas
Question 229
(****) non calculator
The population, P in hundreds, of a herd of zebra t years after a certain instant is
given by the formula
P = 6t +
96
− 60 , t > 0 .
t
a) Find the number of zebra in the herd after 2 1 years.
4
b) Find the time during which the herd’s population is increasing.
P = 1750 , t > 4
Created by T. Madas
Created by T. Madas
Question 230
(****)
x 2 − 3)
(
f ( x) =
x3
2
, x ≠ 0.
a) Show clearly that
f ′ ( x ) = A + Bx −2 + Cx −4 ,
where A , B and C are constants to be found.
b) Find the exact coordinates of the stationary points of f ( x ) and use f ′′ ( x ) to
determine their nature.
c) Show that f ( x ) has two points of inflection and determine their coordinates.
f ′ ( x ) = 1 + 6 x −2 − 27 x −4 , min
(
)
(
) ( )(
3,0 , max − 3,0 , 3, 4 , −3, − 4
3
3
Created by T. Madas
)
