定义域为x > 0.
y = x²/2 - lnx
y' = x - 1/x = (x² -1)/x = (x+1)(x-1)/x = 0
x = -1(舍去)或x = 1
0 < x < 1时: (x² -1) < 0, x > 0, y' = (x² -1)/x, < 0, 递减
x >1时: (x² -1) > 0, x > 0, y' = (x² -1)/x, > 0, 递增
单调递减区间为(0, 1)
定义域为x > 0.
y = x²/2 - lnx
y' = x - 1/x = (x² -1)/x = (x+1)(x-1)/x = 0
x = -1(舍去)或x = 1
0 < x < 1时: (x² -1) < 0, x > 0, y' = (x² -1)/x, < 0, 递减
x >1时: (x² -1) > 0, x > 0, y' = (x² -1)/x, > 0, 递增
单调递减区间为(0, 1)