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Bài tập CALCULUS 29
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Created by T. Madas
Question 110
(***+)
The point A lies on the curve with equation
y = x 2 − 9 x + 13 .
The gradient of the normal to the curve at the point A is
1
.
7
Find an equation of the tangent to the curve at A .
y = 12 − 7 x
Created by T. Madas
Created by T. Madas
Question 111
(***+)
r
h
The figure above shows a closed cylindrical can, of radius r cm and height h cm .
a) If the volume of the can is 330 cm3 , show that surface area of the can, A cm 2 ,
is given by
A = 2π r 2 +
660
.
r
b) Find the value of r for which A is stationary.
c) Justify that the value of r found in part (b) gives the minimum value for A .
d) Hence calculate the minimum value of A .
MP1-A , r ≈ 3.745 , Amin ≈ 264
Created by T. Madas
Created by T. Madas
Question 112
(***+)
The point A ( 2,1) lies on the curve with equation
y=
( x − 1)( x + 2 ) ,
2x
x∈», x ≠ 0 .
a) Find the gradient of the curve at A .
b) Show that the tangent to the curve at A has equation
3x − 4 y − 2 = 0 .
The tangent to the curve at the point B is parallel to the tangent to the curve at A .
c) Determine the coordinates of B .
gradient at A = 3 , B ( −2,0 )
4
Created by T. Madas
