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4. (4 marks) The red contour lines at the right belong to 1.21 the parabolic cylinder 1 z = f (x, y) = 4 -x2 The contour lines are spaced at intervals of z = 0.5. A bug 0.8 is slowly descending the cylinder, starting at the top (0, 0, 1 0.6 4) and the projection of its path on the x-y plane follows the curve 0.4 y = x ( 2 - x) Os x- 2 0.2 This path is sketched at the right on the contour diagram. 0 0.5 1.5 In the 3-D diagram it is sketched in red. At what point is the slope of the bug's path the steepest and what is the slope at that point? Start by using the spacing in the contour diagram to approximately locate the point of greatest negative slope of the path and mark this on the contour diagram