f(x)=1⼀3x^3-a⼀2x^2+bx+c,曲线y=f(x)在点(0,f(0))处的切线方程为y=1

2025-03-16 14:15:21
推荐回答(2个)
回答1:

f'(x)=x^2-ax+b, f'(0)=b, f(0)=c
在点P(0,f(0))处的切线方程为 y-f(0)=f'(0)(x-0)--> y-c=bx, 对比y=1
得:b=0, c=1
f'(x)=x^2-ax
若过点(0,2)可作曲线y=f(x)的三条不同切线, 设为:y-2=f'(x)x--> y=x^3-ax^2+2与f(x)有三个交点: x^3-ax^2+2=1/3x^3-a/2x^2+1, 即 F=4x^3-3ax^2+6=0有三个不等实根
F'=12x^2-6ax=12x(x-a/2), 极值点为0, a/2, 又因为a>0,因此
F(0)=6为极大值
F(a/2)=6-a^3/4为极小值
要使其有3个不同实根,需:F(a/2)<0, 即6-a^3/4<0, 即a>24^(1/3)

回答2:

切线Y=1得fx=1,得C=1
接着Gx求导,求出零点(这里不记得是极致点还是零点,你看看书吧)(含有a的方程),知道递增和递减区间在哪,接着把—2和1带进入看一下就知道答案了

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