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Let f(x,y) = 9y^2 −(3x^2)y denote the temperature at the point (x,y) in the plane, and...

Let f(x,y) = 9y^2 −(3x^2)y denote the temperature at the point (x,y) in the plane, and let C(t) = (t^2, 3t) be the path of a crawling ant in the plane. Find how fast the temperature of the ant is changing at time t = 2.

At time t = 2 the ant is at the point C(2) = (4, 6). Which direction should the ant crawl to warm up as quickly as possible (in the near term)? Please a provide a vector as your answer.

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