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Bài tập Toán DIFFERENTIATION 11
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Created by T. Madas
Question 3
For each of the following equations find the coordinates of their stationary points and
determine their nature.
3
a) y = 12 x − x 2 , x > 0
3
1
b) y = x 2 − 6 x 2 , x > 0
1
c) y = 6 x 2 − 4 x − 2, x > 0
7
d) y = x 2 − 14 x 2 + 100, x > 0
9 1
max ( 4,16 ) , min 2, −4 2 , max , , min ( 4, 4 )
16 4
(
Created by T. Madas
)
Created by T. Madas
Question 4
For each of the following equations find the coordinates of their stationary points and
determine their nature.
3
a) y = x3 − 16 x 2 + 60, x > 0
5
b) y = 5 x 2 − 6 x 3 + 10, x > 0
4
c) y = 6 x 3 − x 2 − 20, x > 0
5
d) y = 5 x 2 − 2 x 2 − 10, x > 0
min ( 4, −4 ) , min (1,9 ) , max ( 8,12 ) , max ( 4,6 )
Created by T. Madas
Created by T. Madas
Question 5
For each of the following equations find the coordinates of their stationary points and
determine their nature.
a) y =
b) y =
1 1
−
, x>0
x
x
3 x −2
3
x2
c) y = 3 x +
d) y =
, x>0
27
, x>0
x
1 2
−3 , x > 0
3 x x
2
min 4, − 1 , max (1,1) , min ( 27, 4 ) , min 2, −
4
3
(
)
Created by T. Madas
