Created by T Madas Question 231 (****) y f ( x) = x+4 x M R O N x The figure above shows the curve C with equation f ( x) = x+4 , x>0 x a) Determine the coordinates of the minimum point of C , labelled as M The point N lies on the x axis so that MN is parallel to the y axis The finite region R is bounded by C , the x axis, the straight line segment MN and the straight line with equation x = b) Use the trapezium rule with strips of equal width to estimate the area of R c) Use integration to find the exact area of R d) Calculate the percentage error in using the trapezium rule to find the area of R e) Explain with the aid of a diagram why the trapezium rule overestimates the area of R C2R , M ( 4, ) , area ≈ 12.7344 , area = 38 , 0.53% Created by T Madas Created by T Madas Question 232 (****) The curve C with equation y = f ( x ) passes through the point P (16, −5 ) , and its gradient function f ′ ( x ) is given by f ′( x ) = x−6 , x>0 x a) Find an equation of the tangent to C at P b) Determine an equation of C The point Q lies on C and the gradient of C at that point is −1 c) Find the coordinates of Q ( C1U , y = x − 90 , y = x − 12 x + , Q 4, − 55 3 Created by T Madas ) Created by T Madas Question 233 (****) y = x2 − y y = 1 − x R O x The figure above shows the graphs of the curves with equations y = x − and y = 1 − x The finite region R is bounded by the two curves in the 1st quadrant, and is shown shaded in the figure above Determine the exact area of R C2V , 16 Created by T Madas