Consider the scalar field f(x,y) = x + kry + y. (a) Show that (0,0) is...

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Consider the scalar field f(x,y) = x + kry + y. (a) Show that (0,0) is a critical point for f(x, y) for any k R. (b) For what values of k will f(x,y) have a saddle point at (0,0). (c) For what values of k does f have local minimum at (0,0)? (d) For what values of k is the Second Derivative Test inconclusive? Consider the scalar field f(x,y) = x + kry + y. (a) Show that (0,0) is a critical point for f(x, y) for any k R. (b) For what values of k will f(x,y) have a saddle point at (0,0). (c) For what values of k does f have local minimum at (0,0)? (d) For what values of k is the Second Derivative Test inconclusive?

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