Question

已知f(x)＝x＋，h(x)＝，設(shè)F(x)＝f(x)－h(x)，求F(x)的單調(diào)區(qū)間與極值．

Answer 1

當(dāng)x∈時(shí)，減函數(shù)；x∈時(shí)，是增函數(shù)．F(x)在x＝時(shí)，有極小值，F＝.

F(x)＝f(x)－h(x)＝x＋－ (x≥0)．
F′(x)＝－＝.
令F′(x)＝0得x＝.
當(dāng)x∈時(shí)，F′(x)<0；x∈時(shí)，F′(x)>0.
故當(dāng)x∈時(shí)，F(x)是減函數(shù)；x∈時(shí)，F(x)是增函數(shù)．
F(x)在x＝時(shí)，有極小值，F＝.