Find the minimum positive period of function f (x) = 2 (sin2x) ^ 2 + 4sin2x * cos2x + 3 (cos2x) ^ 2, and find the minimum and maximum

F (x) = 2 (sin2x) ^ 2 + 4sin2x * cos2x + 3 (cos2x) ^ 2 = 2 (sin2x) ^ 2 + 2sin4x + [2 (cos2x) ^ 2 + cos2x ^ 2] = 2 + 2sin4x + cos2x ^ 2 = 2 + 2sin4x + (cos4x + 1) / 2 = 2.5 + 2sin4x + 1 / 2cos4x = 2.5 + (17 / 4) ^ (1 / 2) sin (4x + a) period 0.5 π, maximum 2.5 + + 17 / 4) ^ (1 / 2), most

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