Created by T Madas Question 200 (****) f ( x ) = x2 + 16 , x ≠ x The curve C has equation y = f ( x ) Show that C has two turning points, of which one is stationary, and the other is a non stationary point of inflection Determine the exact coordinates of each point point of inflection at Created by T Madas ( −16,0) , ( 2,12) Created by T Madas Question 201 (****) y M y = 8x − x2 O A x The figure above shows the quadratic curve with equation y = 8x − x2 , x ∈ » The point M is the maximum point of the curve and the point A is one of the curve’s x intercepts Find the exact area of the shaded region, bounded by the curve, the x axis and the straight line segment from A to M C2J , area = 224 Created by T Madas Created by T Madas Question 202 (****) The point P , whose x coordinate is , lies on the curve with equation y= k + 4x x , x∈» , x > , 7x where k is a non zero constant a) Determine, in terms of k , the gradient of the curve at P The tangent to the curve at P is parallel to the straight line with equation 44 x + y − = b) Find an equation of the tangent to the curve at P MP1-Q , dy dx Created by T Madas = x = 14 − 16k , 44 x + y = 25