已知函数f(x)=x3+ax2+bx+c在点P(-2,f(-2))处的切线方程为y=9x+14,又f(0)=-2
3个回答

f(x)=x3+ax2+bx+c

f'(x)=3x^2+2ax+b

f'(-2)=12-4a+b=9

f(0)=c=-2

因为过(-2,f(-2))处的切线方程应该是:

y-f(-2)=f'(-2)(x+2)=9(x+2)

即 y=9x+18+f(-2)

故:18+f(-2)=14, f(-2)=-4

即:-8+4a-2b+c=-4

联立解得:a=0,b=-3,c=-2

故f(x)=x^3-3x-2

(1) f'(x)=3x^2-3=3(x^2-1)

令f'(x)=0得:x=-1,或x=1

根据f'(x)的正负,可得

f(x)在(-无穷,-1]是增,在[-1,1]上减,在[1,+无穷)上增

当x=-1时,f(x)极大值是f(-1)=0

当x=1 时,极小值是g(1)=-4

(2)F(x)=