设函数f(x)=x(e^x+1)+1/2x^2.则函数f(x)的单调增区间为
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![设函数f(x)=x(e^x+1)+1/2x^2.则函数f(x)的单调增区间为](/uploads/image/z/10758758-14-8.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dx%28e%5Ex%2B1%29%2B1%2F2x%5E2.%E5%88%99%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4%E4%B8%BA)
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设函数f(x)=x(e^x+1)+1/2x^2.则函数f(x)的单调增区间为
设函数f(x)=x(e^x+1)+1/2x^2.则函数f(x)的单调增区间为
设函数f(x)=x(e^x+1)+1/2x^2.则函数f(x)的单调增区间为
f'(x)=xe^x+e^x+1+x
=(x+1)(e^x+1)
e^x+1>0
x>-1,f'(x)>0
单调递增区间(-1,+∞)