Created by T Madas Question 224 (****) f ( x ) = x3 + x − x + 15 , x ∈ » a) Show that ( x + 3) is a factor of f ( x ) The figure below shows the curve C with equation y = f ( x ) y A B y = f ( x) R O x The points A and B are stationary points of C b) Find the exact coordinates of A and B The finite region R is bounded by the curve, the x axis and the straight line segment OA , where O is the origin c) Determine the exact area R ( ) C2G , A ( −1,16 ) , B , 400 , area = 92 27 Created by T Madas Created by T Madas Question 225 (****) The curve C has equation y= x2 + 3x3 , x>0 Show clearly that x2 d2y dx + 6x dy + 6y = dx C1T , proof Question 226 (****) f ( x) ≡ x + x2 , x>0 Find the range of values of x , for which f ( x ) is increasing x>4 Created by T Madas Created by T Madas Question 227 (****) y L R O y = x2 − x + 2 P Q x The diagram above shows the quadratic curve C with equation y = x2 − x + 2 The curve crosses the x axis at the points P and Q , and the y axis at the point R The line L is the tangent to C at the point P a) Find an equation of L b) Find the exact area of the shaded region bounded by the tangent at P , the curve and the y axis y + x = 10 , area = Created by T Madas