f(x)=ln(2+3x)-3/2x^2
g(x)=f(x)+3/2x^2+(m-1)x
=ln(2+3x)+(m-1)x
g'(x)=3/(2+3x)+(m-1)
=[3+(m-1)(2+3x)]/(2x+3)
当m=1时
当x>-2/3 g'(x)>0 g(x)单调增
当x1时 (1+2m)/(3-3m)>-2/3
当 x0 g(x)单调增
当 (1+2m)/(3-3m)0 g(x)单调增
f(x)=ln(2+3x)-3/2x^2
g(x)=f(x)+3/2x^2+(m-1)x
=ln(2+3x)+(m-1)x
g'(x)=3/(2+3x)+(m-1)
=[3+(m-1)(2+3x)]/(2x+3)
当m=1时
当x>-2/3 g'(x)>0 g(x)单调增
当x1时 (1+2m)/(3-3m)>-2/3
当 x0 g(x)单调增
当 (1+2m)/(3-3m)0 g(x)单调增