一道大一的微积分题目Considerthefunctionf(x)=xx;x>0.(a)Findf0(x)andf00(x).(b)Solvef0(a)=0.Isthereanyb>0suchthatf00(b)=(c)Itisclearthatf0(x)<0forx<aandf0(x)>0forx>a.Thereforefisdecreasingon(0;

　　一道大一的微积分题目

　　Considerthefunctionf(x)=xx;x>0.

　　(a)Findf0(x)andf00(x).

　　(b)Solvef0(a)=0.Isthereanyb>0suchthatf00(b)=

　　(c)Itisclearthatf0(x)a.Thereforefisdecreasingon

　　(0;a)andincreasingon(a;1)andsofisnot1􀀀1.Letg(x)=xx;x>a.Explainwhyg

　　is1􀀀1.

　　(d)Find(g􀀀1)0(4).