Identify the monomial function(s) that have a minimum.

A monomial with a positive coefficient and an even exponent is nonnegative for every real x and equals 0 at x = 0, so it has a minimum there. Thus y = 4x⁴, y = 3x², and y = 2x⁶ have minimum value 0. The negative coefficient in y = −2x⁶ makes it decrease without bound, while the odd-power functions do not have a minimum.

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