Given function f (x) = INX, G (x) = ax ^ 2 / 2 + BX (a is not equal to 0) 1. If a = - 2, the function H (x) = f (x) - G (x) is an increasing function in its domain of definition, the value range of real number B is obtained 2. Under the conclusion of 1, let function ψ (x) = e ^ (2x) + be ^ x, X ∈ [0, in2], find the minimum value of function ψ (x) (the minimum value is represented by the formula containing B)

Given function f (x) = INX, G (x) = ax ^ 2 / 2 + BX (a is not equal to 0) 1. If a = - 2, the function H (x) = f (x) - G (x) is an increasing function in its domain of definition, the value range of real number B is obtained 2. Under the conclusion of 1, let function ψ (x) = e ^ (2x) + be ^ x, X ∈ [0, in2], find the minimum value of function ψ (x) (the minimum value is represented by the formula containing B)

1,h(x)=lnx+x^2-bx(x>0),h'(x)=1/x+2x-b=(2x^2-bx+1)/x>0.
2X ^ 2-bx + 1 > 0 holds when x > 0
The opening of 2x ^ 2-bx + 1 is upward, and the axis of symmetry is x = B / 4
If B 0 is true when x > 0
If b > 0, only 2 (B / 4) ^ 2-B (B / 4) + 1 = - B ^ 2 / 8 + 1 > = 0,0