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Bài tập CALCULUS 89
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Created by T. Madas
Question 294
(*****)
The point P lies on the curve with equation y = x 2 , x > 0 .
The finite region bounded by the curve, the tangent to the curve at P and the y axis
has area of 72 square units.
Determine the x coordinate of P .
SP-I , 6
Created by T. Madas
Created by T. Madas
Question 295 (*****)
y
f ( x ) = x 2 − 3x + 18
P
O
1
x
A quadratic curve has equation
y = x 2 − 3 x + 18 , x ∈ » .
The tangent to the curve at the point P meets the x axis at the point with coordinates
(1,0 ) , as shown in the figure above.
Find the area of the finite region bounded by the curve, the coordinates axes and the
tangent to the curve at P , shown shaded in figure above.
MP1-S , area =
Created by T. Madas
229
6
Created by T. Madas
Question 296
(*****)
The curve with equation y = f ( x ) , lies entirely in the first quadrant. The point P ,
whose x coordinate is a lies on this curve.
The tangent to the curve at P meets the x axis at the point A and the y axis at the
point C .
The normal to the curve at P meets the x axis at the point B and the y axis at the
point D .
Given further that the gradient at P is positive, show that the difference between the
areas of the triangle PAB and the triangle PCD is given by
2
1 + f ′ ( a )
2
f ( a ) − a 2 .
2 f ′( a )
SP-G , proof
Created by T. Madas
