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Bài tập CALCULUS 52
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Created by T. Madas
Question 184
(****) non calculator
7
48 + 3 x 3
y=
, x>0.
4 x2
a) Find an expression for
dy
.
dx
b) Show that the value of
dy
1
where x = 8 , is
.
dx
64
dy 1 − 23
= x − 24 x −3
dx 4
Question 185
(****) non calculator
(
)
f ( x ) = 2 x x 2 − 12 x − 16 , x > 0
Find the exact value of f ′ ( 8 ) .
f ′ (8) = 4 2
Created by T. Madas
Created by T. Madas
Question 186
(****)
A curve C has equation
y=
3 x −2
3
x2
, x>0.
a) Find the coordinates of the stationary point of C , and determine its nature.
The curve has a non stationary turning point, P .
b) Determine the coordinates of P .
(
max at (1,1) , P 25 , 112
16 125
Created by T. Madas
)
Created by T. Madas
Question 187
(****)
y
O
y=
A
x 4 − 10 x 2 + 9
x2
B
R
x
The figure above shows the graph of the curve with equation
y=
x 4 − 10 x 2 + 9
x2
, x>0.
The curve meets the x axis at the points A and B .
The finite region R , shown shaded in the figure above, is bounded by the curve and
the x axis.
Find the exact area of R .
16
3
Created by T. Madas
