如图，在曲线[tex=2.286x1.429]qOD0bBSg/KT4jxyhefRIrw==[/tex]上取一点[tex=0.643x1.0]Ft8KOBgb78fnKY0jEt4Rsg==[/tex]，过[tex=0.643x1.0]Ft8KOBgb78fnKY0jEt4Rsg==[/tex]的切线与该曲线交于[tex=0.857x1.214]ChdusW5rAupjge6v/DGHRA==[/tex]，证明：曲线在[tex=0.857x1.214]ChdusW5rAupjge6v/DGHRA==[/tex]处的切线斜率恰好是在[tex=0.643x1.0]Ft8KOBgb78fnKY0jEt4Rsg==[/tex]处切线斜率的四倍。[img=124x125]1772d9b8d57eb84.png[/img]
举一反三
- 试证明[tex=3.0x1.214]IUHrYHrM08MGOPGYrhrf7lrE2bY1p1ex4nRajltli6M=[/tex]，[tex=0.857x1.214]ChdusW5rAupjge6v/DGHRA==[/tex]逻辑蕴含[tex=0.643x1.0]Ft8KOBgb78fnKY0jEt4Rsg==[/tex]
- 设集合[tex=0.643x1.0]Ft8KOBgb78fnKY0jEt4Rsg==[/tex]和[tex=0.857x1.214]ChdusW5rAupjge6v/DGHRA==[/tex],且[tex=9.0x1.286]UAF5zept/c62KMXELvSGGfAwG2qylwDgM7o3RINViA7TqPJDrBVi4FZZoSvYhlYI[/tex]证明:[tex=12.071x1.357]Y5IiK8bdaDJGfIwXCUX7R+ai677sJrHfojsrCo44sxQa1ewkG9Ld67z46GhxKM5x4OQU6RpwKU97q00GHnSsTyB2cV6HJ+TgOtJRqh0Puco=[/tex]
- 设集合[tex=0.643x1.0]Ft8KOBgb78fnKY0jEt4Rsg==[/tex]和[tex=0.857x1.214]ChdusW5rAupjge6v/DGHRA==[/tex],且[tex=9.0x1.286]UAF5zept/c62KMXELvSGGfAwG2qylwDgM7o3RINViA7TqPJDrBVi4FZZoSvYhlYI[/tex]证明:[tex=7.857x2.0]ml3J+0hEclGfkoBj6hNrTkcUsziUVX4exOX2EeHgRFEUQEqpiFbezmamaoXwQi/j[/tex]
- 在曲线[tex=2.286x1.429]sraiNwH0IhPMSW9KtxLfMg==[/tex]上取一点 [tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex]，过[tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex]的切线与该曲线交于[tex=0.786x1.286]gvyykdQdNBydRqWi9I4iuA==[/tex]， 证明：曲线在[tex=0.786x1.286]gvyykdQdNBydRqWi9I4iuA==[/tex]处的切线斜率正好是在[tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex]处切线斜率的4倍。
- 一曲线过点(1,0)且曲线上任一点[tex=2.929x1.357]25jAdQ4EVKhlk22U111yAg==[/tex] 处的切线在[tex=0.5x1.0]yBR4oiFoTexGaFalQ7m8kg==[/tex] 轴上的截距等于[tex=0.643x1.0]Ft8KOBgb78fnKY0jEt4Rsg==[/tex]点与原点的距离.求该曲线的方程.