Bài tập CALCULUS 90

Created by T Madas Question 297 (*****) The points A and B are stationary points of the curve with equation y = x + x − 12 x + k , x ∈ » , where k is a constant Given that y = 37 at the point of inflexion of the curve, show that the area of the region bounded by the curve and the straight line through A and B is 16 SP-M , proof Created by T Madas Created by T Madas Question 298 (*****) A quadratic curve has equation y = ax + bx + c , a ≠ , where a , b and c are constants The curve meets the x axis at A ( −2,0 ) and has a maximum point at B ( 0,1) The point C lies on the curve so that AB is perpendicular to BC Determine the area of the finite region bounded by the curve and the straight line segment AC SP-U , proof Created by T Madas Created by T Madas Question 299 (*****) The rate of change, with respect to x , of the gradient of a curve is constant The curve passes through the points with coordinates (1, ) and ( −3,0 ) , the gradient at the former point being − Show that the area of the finite region bounded between the curve and the straight line 125 with equation y = x is SP-A , proof Created by T Madas