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Bài tập Toán DIFFERENTIATION 18
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Created by T. Madas
Question 16
The curve C has equation
y = 2 x3 − 6 x 2 + 3x + 5 .
The point P ( 2,3) lies on C and the straight line L1 is the tangent to C at P .
a) Find an equation of L1 .
The straight lines L2 and L3 are parallel to L1 , and they are the respective normals to
C at the points Q and R .
b) Determine the x coordinate of Q and the x coordinate of R .
y = 3x − 3 , x = 1 , 5
3 3
Created by T. Madas
Created by T. Madas
Question 17
y
(
y = 1 x 2 − 12 x + 35
4
)
R
L1
Q
P
O
x
S
L2
The figure above shows the curve with equation
(
)
y = 1 x 2 − 12 x + 35 .
4
The curve crosses the x axis at the points P ( x1,0 ) and Q ( x2 ,0 ) , where x2 > x1 .
The tangent to the curve at Q is the straight line L1 .
a) Find an equation of L1 .
The tangent to the curve at the point R is denoted by L2 . It is further given that L2
meets L1 at right angles, at the point S .
b) Find an equation of L2 .
c) Determine the exact coordinates of S .
(
C1Q , y = 1 x − 7 , 4 y + 8 x = 31 , S 9 , − 5
2 4
2
2
Created by T. Madas
)
Created by T. Madas
Question 18
The point P (1,0 ) lies on the curve C with equation
y = x3 − x , x ∈ » .
a) Find an equation of the tangent to C at P , giving the answer in the form
y = mx + c , where m and c are constants.
The tangent to C at P meets C again at the point Q .
b) Determine the coordinates of Q .
y = 2 x − 2 , Q ( −2, −6 )
Created by T. Madas
