Created by T Madas Question 106 (***+) The curve C has equation y = x3 − x + 24 x − 19 , x ∈ » a) Show that the tangent to C at the point P , where x = , has gradient b) Find the coordinates of another point Q on C at which the tangent also has gradient The normal to C at Q meets the coordinate axes at the points A and B c) Show further that the approximate area of the triangle OAB , where O is the origin, is 11 square units Q ( 5,1) Created by T Madas Created by T Madas Question 107 (***+) y y = x2 − x + C ( 7,12 ) O A B x The diagram above shows the curve with equation y = x2 − x + The point C ( 7,12 ) lies on the curve while A and B are the points of intersection of the curve and the x axis Find the exact area of the shaded region, bounded by the curve, the straight line segment AC and the x axis C2M , area = 76 Created by T Madas Created by T Madas Question 108 (***+) y= x (3 x + 1) x2 , x >0 Show clearly that y dx = 15 proof Question 109 (***+) The gradient of every point on the curve C , with equation y = f ( x ) satisfies f ′ ( x ) = 3x − x + k , where k is a non zero constant The points P ( 0, −3) and Q ( 2,7 ) both lie on C Find an equation for C y = x3 − x + x − Created by T Madas