Consider f e C} (R") and the following function 1 Hy (æ, z) = f(z) + Vf(z)"(x – z) + ||x – z||3, 27 where x, z E R" and 0 < y < 1/L. (a) Show that the following two statements are true Hy (x, z) > f(æ) for every æ, z E R" Hy (x, x) = f(x) for every æ E R".

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