Created by T Madas Question 72 (***) y S P O Q R x The figure above shows the graph of the quadratic curve C with equation y = 3x − x + The curve crosses the x axis at the points P and Q a) Find the coordinates of P and Q b) Show clearly that  x − x + dx = The point R lies on the x axis where x = and the point S lies on C so that RS is parallel to the y axis c) Find the area of the shaded region ( ) P (1,0 ) , Q , Created by T Madas 27 Created by T Madas Question 73 (***) A cubic curve has equation f ( x ) = x3 − x + x + The point P ( 2,1) lies on the curve a) Find an equation of the tangent to the curve at P The point Q lies on the curve so that the tangent to the curve at Q is parallel to the tangent to the curve at P b) Determine the x coordinate of Q y = x − , xQ = Created by T Madas Created by T Madas Question 74 (***) y y = x+4 B A y = x2 − 3x + x O The figure above shows a curve C and a straight line L with respective equations y = x − 3x + and y = x + The curve and the straight line meet at the points A and B a) Find the coordinates of A and B b) Find the exact area of the finite region bounded by C and L , shown shaded in the figure above A (1,5 ) , B ( 3, ) , area = Created by T Madas