已知函数y=x대-4x눀+5x-4,求过点(2,-2)的曲线y的切线方程 求详细过程^ω

2025-06-29 08:54:25
推荐回答(1个)
回答1:

f'(x)=3x^2-8x+5
∴k=(3x-5)(x-1)
k(x-2)=y+2
y=x^3-4x^2+5x-4
(3x-5)(x-1)(x-2)=y+2
(3x-5)(x-1)(x-2)=(x^3-4x^2+5x-4)+2
(3x-5)(x-1)(x-2)=x^3-4x^2+5x-2
(3x-5)(x-1)(x-2)=(x-2)(x^2-2x+1)
(x-2)(3x^2-8x+5-x^2+2x-1)=0
(x-2)(2x^2-6x+4)=0
(x-2)(x^2-3x+2)=0
(x-2)^2(x-1)=0
x1=2,x2=1
很容易的得到答案是切点是(2,-2)或者是(1,-2)
y=x-4
或者y=-2,