设函数y=y（x）由参数方程x＝t3+3t+1y＝t3−3t+1确定，求y=y（x）的单调区间、极值点、凹凸区间、拐点、渐近线．

Question

设函数y=y（x）由参数方程

x＝t3+3t+1

y＝t3−3t+1

确定，求y=y（x）的单调区间、极值点、凹凸区间、拐点、渐近线．

Answer 1

求导数dydt＝3t2−3，dxdt＝3t2+3＞0dydx＝t2−1t2+1ddtdydx＝2t(t2+1)−2t(t2−1)(t2+1)2＝4t(t2+1)2d2ydx2＝4t3(t2+1)3，dydx＝t2−1t2+1＞0，t＜−1＝0，t＝−1＜0，−1＜t＜1＝0，t＝1＞0，t＞1d2ydx2＝4t3(t2+1...