已知f(x)=x∣x∣1+x,求f(x)的凹凸性及渐近线.\text{已知}f(x)=\frac{x\left|x\right|}{1+x}\text{,求}f(x)\text{的凹凸性及渐近线}.
凹区间(−∞,−1),(0,+∞),凸区间(−1,0).斜渐近线是y=x−1,y=−x−1.\text{凹区间}\left(-\infty,-1\right),\left(0,+\infty\right),\text{凸区间}\left(-1,0\right).\text{斜渐近线是}y=x-1,y=-x-1.
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