Bài tập CALCULUS 44

Created by T Madas Question 161 (***+) y Q (1,0 ) O R x P The figure above shows the graph of a cubic curve, which touches the x axis at the point Q (1,0 ) a) Determine an equation for the cubic curve , given its gradient function is dy = x − 12 x + dx The cubic curve crosses the x axis and the y axis at the points R and P , respectively b) Determine the coordinates … i … of the point P ii … of the point R C1I , y = x3 − x + x − , P ( 0, −4 ) , R ( 4,0 ) Created by T Madas Created by T Madas Question 162 (***+) y C L R Q P x O The figure above shows a sketch of the curve C with equation y = 2x2 , x ∈ » ( ) The straight line L passes through the points P , and Q ( 0,1) , where the point 2 P lies on C The straight line L meets C again, at the point R a) Find the coordinates of R The tangents to C at the points P and R meet at the point T ( ) b) Show that the coordinates of T are − , −1 R ( −1, ) Created by T Madas Created by T Madas Question 163 (***+) A cubic curve has equation y = x3 − x + , x ∈ » The point P lies on the curve where x = Show that the normal to the curve at P does not meet the curve again SYN-R , proof Created by T Madas