Question

微分法:求曲线的一条法线的方程

Answer 1

y=x(2x-3)^2 dy/dx = (x)' (2x-3)^2 + (x) [(2x-3)^2]' dy/dx = (2x-3)^2 + x [ 2(2x-3)^(2-1) * (2x-3)' ] dy/dx = (2x-3)^2 + x [ 2(2x-3) * 2 ] dy/dx = (2x-3)^2 + 4x(2x-3) = 3(2x-3)(2x-1) ∵L的斜度=-3 ∴dy/dx = -3 3(2x-3)(2x-1) = -3 4x^2 - 8x + 4 = 0 (x-1)^2 = 0 x = 1 当 x = 1 时，y=(1) [2*(1) - 3]^2 = 1 法线的斜度 = -1/(-3) = 1/3 ∴法线的方程为 y - 1 = (1/3)(x - 1) y = x/3 + 2/3 2014-05-27 21:47:17 补充： 谢 谢 = ] 2014-05-27 21:49:05 补充： 你也可在 意见区 看看 知足常乐 知识长 的回答
L: y = -3x - 5 斜率 = -3 C: y = x(2x - 3)² 　　= x(4x² - 12x + 9) 　　= 4x³ - 12x² + 9x dy/dx = 12x² - 24x + 9 法线垂直于 L 切线水平于 L 切线斜率 = -3 dy/dx = 12x² - 24x + 9 = -3 12x² - 24x + 12 = 0 x² - 2x + 1 = 0 (x - 1)² = 0 x = 1 C: x = 1 即 y = 1 法线斜率 = -1/-3 = 1/3 2014-05-27 21:44:36 补充： 法线方程： y - 1 = (1/3)(x - 1) 3y - 3 = x - 1 x - 3y + 2 = 0 2014-05-27 22:33:43 补充： Cheers! (◕‿◕)