f(x)=(1/2)x^2+lnx.当(1,+∞)求证f(x)
问题描述：
f(x)=(1/2)x^2+lnx.当(1,+∞)求证f(x)
答
g(x)=f(x)-(2/3)x^3+1/6=-(2/3)x^3+(1/2)x^2+1/6+lnxg'(x)=-2x^2+x+1/x-2x^2+x=-2(x-1/4)^2+1/8开口向下,对称轴x=1/4所以x>1时,定义域在对称轴右边,-2x^2+x是减函数反比例函数y=1/x在x>1也是减函数所以g'(x)=-2x^2+x...