[分析]f is differentiable on R,f'(x)>f(x) and f(0)=0

看板Math作者 (linshihhua)時間14年前 (2011/06/03 23:58), 編輯推噓2(2推 0噓 1→)
留言3則, 2人參與, 最新討論串1/1
let f be a real-valued differentiable function on R such that f'(x)>f(x) for all x in R. Assume that f(0)=0, show that f(x)>0 for all x>0 -- ● ● 李ㄆㄧㄚˋ眉頭一皺! ◢███◣ ████ ◢████◣ ◢ ██ ◣ 驚覺南方公園早被停播! ▂▂▂▂▂ ◢████◣ ██████ █◤ ◥█ 深深覺得黑棒一定不清純! ㄟˇㄏ◤ █ ㄟˇㄏ █ ㄟˇㄏ █ㄟˇㄏ█ 原創 ψindiaF4 Happy ㄧ..ㄧ █ ㄧ..ㄧ █ ㄧ..ㄧ █ㄧ..ㄧ█ ψdiabloq13 Push ◥ /︷\ ◢ ◥ /︷\ ◤ ◥ /︷\ ◢ ◥.◣◢.◤ 改圖 ψfreefrog Doll -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 218.170.50.27
推
06/04 00:16, , 1F
f'(0)>f(0)=0, 局部遞增, f(c)>0 for c>0
06/04 00:16, 1F
推
06/04 00:17, , 2F
g(x)= exp(-x)f(x), g(0)=0, g'(x)>0 for all x >0
06/04 00:17, 2F
→
06/04 00:18, , 3F
hence, g(x)>0 for all x >0
06/04 00:18, 3F
‣ 更多 linshihhua 的文章
文章代碼(AID): #1DwGIkkZ (Math)