已知函数f(x)=1/2x^2-3x+2lnx,在区间[1,4]上的最大值为

问题描述:

已知函数f(x)=1/2x^2-3x+2lnx,在区间[1,4]上的最大值为

f(x) = (1/2)x^2-3x+ 2lnxf'(x) = x-3 +2/x =0x^2 -3x -2 =0x = (3+√17)/2or (3-√17)/2( rejected)f''(x) = 1-2/x^2f''((3+√17)/2) >0 ( min )f(1) = 1/2 - 3 +0 = - 5/2f(4) = 2 - 6 + 2ln2 = -4+2ln2 > f(1...