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Given lim (x -> inf) f(x) = lim (x -> -inf) f(x) = 0, and f(x) continuous over R, Show that (edit:)if there is a number z such that f(z) > 0 then f attains a maximum value on R. I know why intuitively but i dunno how 2 express it mathematically. some help would b greatly appreciated. thanx