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)=