已知函数f(x)=x^2/x+1,(1)若f(x)在点(1,f(1))处的切线斜率为1/2,求实数a的值,(2)若f(x)在x=1处

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已知函数f(x)=x^2/x+1,(1)若f(x)在点(1,f(1))处的切线斜率为1/2,求实数a的值,(2)若f(x)在x=1处
已知函数f(x)=x^2+a/x+1,((2)若f(x)在x=1处 取得极值,求函数f(x)的单调区间

(1)f(x)=(x^2+a)/(x+1)f'(x) = [(x^2+a)- 2(x+1)x ]/ (x+1)^2f'(1) = (1+a -4)/4 = 1/2-3+a = 2 a = 5(2)f'(1) = 0=> (1+a -4)/4 = 0a = 3f'(x) = [(x^2+3)- 2(x+1)...