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Bài tập CALCULUS 41
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Created by T. Madas
Question 152
(***+)
The point P ( 3, k ) lies on the curve with equation
y = x 2 + ax − 4 ,
where a and k are constants.
Given that the gradient at P is 3 determine the value of a and the value of k .
SYN-G , a = −3, k = −4
Created by T. Madas
Created by T. Madas
Question 153
(***+)
The curve C has equation
y = x3 − 4 x 2 + 6 x − 4 .
a) Find an equation of the normal to C at the point P ( 3,5 ) .
The point Q lies on C so that the normal to the curve at Q is parallel to the normal to
the curve at P .
b) Find an equation of the normal to the curve at Q .
x + 9 y = 48 , 3 x + 27 y + 176 = 0
Created by T. Madas
Created by T. Madas
Question 154
(***+)
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) Find the coordinates of Q .
y = 2 x − 2 , Q ( −2, −6 )
Created by T. Madas
