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Bài tập Toán DIFFERENTIATION 20
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Created by T. Madas
Question 22
A curve has equation
y = 6 3 x5 − 15 3 x 4 − 80 x + 16 ,
x∈» ,
x ≥ 0.
Find the coordinates of the stationary point of the curve and determine whether it is a
local maximum, a local minimum or a point of inflexion.
local minimum at (16, −2800 )
Created by T. Madas
Created by T. Madas
Question 23
A curve has equation
y = x2 − 6 x
3
x +2,
x∈» ,
x ≥ 0.
Find the coordinates of the stationary points of the curve and classify them as local
maxima, local minima or a points of inflexion.
local minimum at ( 8, −30 ) , local maximum at ( 0, 2 )
Created by T. Madas
Created by T. Madas
Question 24
A curve has equation
(
)
y = x x 2 − 128 x ,
x∈» ,
x>0.
(
)
The curve has a single stationary point with coordinates 2α , − 2β , where α and β
are positive integers.
Find the value of β and justify that the stationary point is a local minimum.
β = 12
Created by T. Madas
