Question

已知函数f(x)=0.5x^2-alnx(a∈R)问，1.求函数的单调区间。2.设g(x)=f(x)+2x,若g(x)在

Answer 1

(1)

定义域x > 0

f'(x) = x - a/x = (x² - a)/x

(i) a = 0, f(x) = x²/2, 为开口向上的抛物线，对称轴x = 0, x > 0: f(x)为增函数

(ii) a < 0, f'(x) > 0, f(x)为增函数

(iii) a > 0, f'(x) = 0, x = √a (舍去x...