Created by T Madas Question 234 (****) The curve C has equation y = x3 − 3x + , x ≠ x The point P ( 2,12 ) lies on C a) Find the gradient at P b) Determine the coordinates of another point Q that lies on C , so that the gradient at Q is the same gradient as P C1T , gradient = 20 , Q ( −2, −12 ) Created by T Madas Created by T Madas Question 235 (****) y ( 0,1) x + y =1 R O (1,0 ) x The figure above shows the curve with equation x + y = , x ∈ » , ≤ x ≤ The curve meets the coordinate axes at the points (1,0 ) and ( 0,1) The finite region R is bounded by the curve and the coordinate axes Show that the area of R is SYN-I , proof Created by T Madas Created by T Madas Question 236 (****) non calculator The curve C has equation y= x2 + , x>0 x Show that an equation of the tangent to C at the point where x = is 4 x − 16 y + 21 = proof Created by T Madas