Figure 3 shows the curves y = x and y = which intersect at point P....

  

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Figure 3 shows the curves y = x and y = which intersect at point P. The line x = 6 and line I, which is the tangent to the curve y = at point P, are also shown. a) Find the coordinates of point P b) Find the equation of line! c) Confirm that line I meets the x-axis at (4,0) d) Find the area, which is shaded on the diagram, that is bounded by the curve y = =, the x-axis, line I and the line x = 6 e) Find the non-zero value of x when the gradients of the curves y = x and y = are perpendicular to each other. [2] [3] [1] [6] [3] O y = > +x* Figure 3 11 x = 6 Figure 3 shows the curves y = x and y = which intersect at point P. The line x = 6 and line I, which is the tangent to the curve y = at point P, are also shown. a) Find the coordinates of point P b) Find the equation of line! c) Confirm that line I meets the x-axis at (4,0) d) Find the area, which is shaded on the diagram, that is bounded by the curve y = =, the x-axis, line I and the line x = 6 e) Find the non-zero value of x when the gradients of the curves y = x and y = are perpendicular to each other. [2] [3] [1] [6] [3] O y = > +x* Figure 3 11 x = 6