Created by T Madas Question 294 (*****) The point P lies on the curve with equation y = x , x > The finite region bounded by the curve, the tangent to the curve at P and the y axis has area of 72 square units Determine the x coordinate of P SP-I , Created by T Madas Created by T Madas Question 295 (*****) y f ( x ) = x − 3x + 18 P O x A quadratic curve has equation y = x − x + 18 , x ∈ » The tangent to the curve at the point P meets the x axis at the point with coordinates (1,0 ) , as shown in the figure above Find the area of the finite region bounded by the curve, the coordinates axes and the tangent to the curve at P , shown shaded in figure above MP1-S , area = Created by T Madas 229 Created by T Madas Question 296 (*****) The curve with equation y = f ( x ) , lies entirely in the first quadrant The point P , whose x coordinate is a lies on this curve The tangent to the curve at P meets the x axis at the point A and the y axis at the point C The normal to the curve at P meets the x axis at the point B and the y axis at the point D Given further that the gradient at P is positive, show that the difference between the areas of the triangle PAB and the triangle PCD is given by + f ′ ( a ) f ( a ) − a f ′( a ) SP-G , proof Created by T Madas