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Bài tập Toán DIFFERENTIATION 19
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Created by T. Madas
Question 19
A curve C with equation
y = 4 x3 + 7 x 2 + x + 11 , x ∈ » .
The point P lies on C , where x = −1 .
a) Find an equation of the tangent to C at P .
The tangent to C at P meets C again at the point Q .
b) Determine the x coordinate of Q .
y = 12 − x , xQ = 1
4
Created by T. Madas
Created by T. Madas
Question 20
y
L1
y = 2 x2 − x + 3
Q
P
R
O
x
L2
The figure above shows the curve C with equation
y = 2 x2 − x + 3 .
C crosses the y axis at the point P . The normal to C at P is the straight line L1 .
a) Find an equation of L1 .
L1 meets the curve again at the point Q .
b) Determine the coordinates of Q .
The tangent to C at Q is the straight line L2 .
L2 meets the y axis at the point R .
c) Show that the area of the triangle PQR is one square unit.
y = x + 3 , Q (1, 4 )
Created by T. Madas
Created by T. Madas
Question 21
y
y = 2 x3 + 3x 2 − 11x − 6
O
Q
P
R
x
The figure above shows the curve C with equation
y = 2 x3 + 3x 2 − 11x − 6 .
The curve crosses the x axis at the points P , Q and R ( 2,0 ) .
The tangent to C at R is the straight line L1 .
a) Find an equation of L1 .
The normal to C at P is the straight line L2 .
The straight lines L1 and L2 meet at the point S .
b) Show that
PSR = 90° .
y = 25 x − 50
Created by T. Madas
