Consider the function

(a) Analytically verify that the level curve of f(x, y) at the level c = 2 is a circle.(b) At the point (√3, 2) on the level curve for which c = 2, sketch the vector showing the direction of the greatest rate of increase of the function. To print a graph of the level curve, go to MathGraphs.com.(c) At the point (√3, 2) on the level curve for which c = 2, sketch a vector such that the directional derivative is 0.(d) Use a computer algebra system to graph the surface to verify your answers in parts (a)–(c).

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f(x, y) = 8y 1 + x² + y²