Bài tập Toán DIFFERENTIATION 18

Created by T Madas Question 16 The curve C has equation y = x3 − x + 3x + 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 − , x = , 3 Created by T Madas Created by T Madas Question 17 y ( y = x − 12 x + 35 ) R L1 Q P O x S L2 The figure above shows the curve with equation ( ) y = x − 12 x + 35 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 = x − , y + x = 31 , S , − 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 = x − , Q ( −2, −6 ) Created by T Madas ... coordinates of S ( C1Q , y = x − , y + x = 31 , S , − 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