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Black Book Advanced Problems in MathematicsMathematicsApplication of Derivatives

array |l|l| Column-I & Column-II (A) ( ⁻¹ x)^ ⁻¹ x - ( ⁻¹ x)^ ⁻¹ x x ( 1, 1) & (P) Always positive (B) ( x)^ x - ( x)^ x x ( 4 , 2 ) & (Q) Always negative (C) ( x)^ x - ( x)^ x x (0, 2 ) & (R) May be positive or negative for some values of x (D) ( ( x))^ ( x) - ( x)^ x x (e^e, ) & (S) May result in zero for some of values of x & (T) Indeterminate array

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