设函数f(x),g(x)在x=x 0 有连续的二阶导数且f(x 0 )=g(x 0 ),f'(x 0 )=g'(x 0 ),f''(x 0 )=g''(x 0 )≠0,说明这一事实的几何意义.
【正确答案】正确答案:曲线y=f(x),y=g(x)在公共点M 0 (x 0 ,f(x 0 ))即(x 0 ,g(x 0 ))处相切,在点M 0 的某邻域有相同的凹凸性.因f''(x),g''(x)在x 0 处连续,f''(x 0 )=g''(x)>0(或<0) x 0 的某邻域(x 0 -δ,x 0 +δ),当x∈(x 0 -δ,x 0 +δ)时f''(x)>0,g''(x)>0(或f''(x)<0,g''(x)<0).又由曲率计算公式知,这两条曲线在点M 0 处有相同的曲率
【答案解析】