Question 3 Describe and sketch the contour plot of z = f(x,y) = 4x2 + y? using level curves of heights c = 0,1,2,3,4, 5. To help you visualise, let x = 0, so that we have a parabola in the y, z -plane and then let y = 0 so we have a parabola in the x, z-plane. What is the parabola vertex? How is it orientated? The graph of the surface is z = 4x2 + y? is the paraboloid so we can expect the contour plot to be a family of ellipses centred at the origin - sketch this. The level curve of height z = c has the equation 4x2 + y² = c . If c = 0 then the graph is the single point (0,0). Can you explain why? For c > 0 we can rewrite the equation as
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