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
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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](/uploads/image/z/5638944-48-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dx%5E2%EF%BC%8Fx%2B1%2C%EF%BC%881%EF%BC%89%E8%8B%A5f%28x%29%E5%9C%A8%E7%82%B9%EF%BC%881%2Cf%281%29%EF%BC%89%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E6%96%9C%E7%8E%87%E4%B8%BA1%EF%BC%8F2%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC%2C%EF%BC%882%EF%BC%89%E8%8B%A5f%28x%29%E5%9C%A8x%3D1%E5%A4%84%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dx%5E2%2Ba%EF%BC%8Fx%2B1%2C%EF%BC%88%EF%BC%882%EF%BC%89%E8%8B%A5f%28x%29%E5%9C%A8x%3D1%E5%A4%84+%E5%8F%96%E5%BE%97%E6%9E%81%E5%80%BC%EF%BC%8C%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4)
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
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
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)^2
f'(1) = (1+a -4)/4 = 1/2
-3+a = 2
a = 5
(2)
f'(1) = 0
=> (1+a -4)/4 = 0
a = 3
f'(x) = [(x^2+3)- 2(x+1)x ]/ (x+1)^2
= [-x^2-2x+3]/(x+1)^2
put f'(x) = 0
-x^2-2x+3 =0
-(x+3)(x-1) = 0
x = 1 or -3
f''(x) =[(-x^2-2x+3)2(x+1) - (x+1)^2(-2x-2)]/(x+1)^4
f''(1) = [0- 4(-4)]/16 = 1 >0 (min)
f''(-3)
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