I'll give you a hint for (c) for starters.
Both ends of a quartic go off in the same direction: either both to or to .
So there's a point where it's at its minimum (in the first case) or maximum (in the second).
Add a big number to the first type of quartic so as to move the minimum above the line y = 0. Subtract a big one from the second so as to move the maximum below the line y = 0.
You will probably need to translate the above into more formal and rigorous language.