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The answer is not correct. For x∈[0,1], minimum value of the expression is 0 for x = 0 or 1. 0.03456 is only correct when x∈(0,1).
since the expression is equal to 0 when x = 0, 1 i don’t think it would make sense to say there is a minimum value of this expression when x ∈ (0,1) because the expression can get arbitrarily close to 0
also 0.03456 is the maximum not minimum so i guess the question meant to ask for the maximum value