If the function f (x) = x · (x-C) 2 has a maximum at x = 2, then the value of constant C is () A. 6B. 2C. 2 or 6D. 23

If the function f (x) = x · (x-C) 2 has a maximum at x = 2, then the value of constant C is () A. 6B. 2C. 2 or 6D. 23

∵ f ′ (x) = (x-C) 2 + 2x (x-C), ∵ function f (x) = x · (x-C) 2 has a maximum at x = 2, ∵ (2-C) 2 + 4 (2-C) = 0, the solution is C = 2 or C = 6; after testing, C = 6, so a