Question: For the following problems, let F(x, y)=x ky, x + y 2. Part (a) For what value(s) of k is the vector field F conservative?

For the following problems, let F(x, y)=x ky, x + y 2. Part (a) For what value(s) of k is the vector field F conservative? Justify your answer. Part (b) Find a potential function f for F(i.e. find f such that F=f) for the value of k which makes F conservative. Part (c) When k =2, compute the work done by F on a particle travelling upwards along the curve y = x 2 from x =1 to x =2.

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