Created by T Madas Question 164 (***+) The curve C has equation y = ax3 + bx − 10 , where a and b are constants The point A ( 2, ) lies on C Given that the gradient at A is , determine the value of a and the value of b a = −2 , b = Created by T Madas Created by T Madas Question 165 (***+) 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 C1O , y = x − , x = , 3 Created by T Madas Created by T Madas Question 166 (***+) The point P ( 2,9 ) lies on the curve C with equation y = x3 − x + x + , 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 point Q also lies on C so that the tangent to C at Q is perpendicular to the tangent to C at P b) Show that the x coordinate of Q is 6+ C1R , y = x + Created by T Madas