For x = 0 to be a local minimum we need to have f(0) the smallest value in an open neighborhood about x = 0. Now, f(0) = 2, and this is smaller than any f(x) with x<0. So far, so good. Now we need to arrange a k value such that f(x) for x near 0 is greater than 2. Thus we need k>2.

-Dan