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Bài tập CALCULUS 55
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Created by T. Madas
Question 194
(****)
The point A ( p, q ) lies on the curve with equation
y = 2 x3 − 4 x 2 + 2 x − 1 .
The tangent to the curve at A has equation
x + 2 y +1 = 0 .
Find the coordinates of A .
(
C1P , A 1 , − 3
2 4
Created by T. Madas
)
Created by T. Madas
Question 195 (****) non calculator
The population, P in thousands, of a colony of wild bees, t weeks after a certain
instant, is given by the formula
P = 16 t +
27
, 0 < t < 16 .
t
a) Calculate the number of bees in the colony after 2 1 weeks.
4
b) Find the range of values of t during which the bees’ population is increasing.
C2U , P = 36000 , 9 < t < 16
4
Created by T. Madas
Created by T. Madas
Question 196
(****)
A curve has equation
(
)
y = x x 2 − 128 x ,
x∈» ,
x>0.
(
)
The curve has a single stationary point with coordinates 2α , − 2 β , where α and β
are positive integers.
Find the value of β and justify that the stationary point is a local minimum.
MP1-O , β = 12
Created by T. Madas
