H1 maths Graph

18/01. The curve C has equation y = - In(x + 3) (1) Sketch the curve, stating the coordinates of any points of intersections with the axes and the equations of any asymptotes parallel to the y-axis. (ii) Find the numerical value of the gradient of C at the point where x = 3. [3] [1] (iii) Find the equation of tangent to C at the point where x = 3 . Give your answer in the form y = mx + c , with m and c correct to 3 significant figures. [2] (iv) Using the equation of tangent found in part (iii), find the numerical value of the area bounded by C, the tangent and the x-axis where x > 0. [3] [2018/MI/04]