Question

设f(x)=|(x-1)²(x+1)³|，求f'（x）

Answer 1

希望有所帮助

追答

拍个清楚的

Answer 2

f(x)
=|(x-1)^2.(x+1)^3|
= (x-1)^2. (x+1)^2.|x+1|
ie
f(x)
= (x-1)^2. (x+1)^3 ; x≥-1
=-(x-1)^2. (x+1)^3 ; x<-1
f(-1) =0
f(-1+)=lim(x->-1+) f(x) =0
f(-1-)=lim(x->-1-) f(x) =0
x=-1, f(x) 连续
f'(-1+)
=lim(h->0) [(h-1-1)^2. (h-1+1)^3 -f(1) ]/h
=lim(h->0) (h-2)^2. h^2
=0
f'(-1-)
=lim(h->0) [-(h-1-1)^2. (h-1+1)^3 -f(1) ]/h
=lim(h->0) -(h-2)^2. h^2
=0
=f'(-1+)
ie
x≥-1
f(x) =(x-1)^2. (x+1)^3
f'(x)
=2(x-1) (x+1)^3 +3(x-1)^2. (x+1)^2
= (x-1)(x+1)^2.[ 2(x+1) +3(x-1) ]
= (x-1)(x+1)^2.(5x-1)
x<-1
f'(x) =-(x-1)(x+1)^2.(5x-1)