19復 忦審晅偒嬌抣



student僷僢働乕僕偺extrema僐儅儞僪傪梡偄傞偲丄忦審晅偒嬌抣傪媮傔傞偙偲偑偱偒傑偡丅
椺偊偽丄忦審g(x,y)=x2+(y2/4)=1偺壓偱偺娭悢f(x,y)=xy偺嬌抣傪媮傔傞偵偼師偺傛偆偵擖椡偟傑偡丅

>with(student):

>extrema(x*y,x2+y2/4=1,{x,y},'s')
(忦審晅偒嬌抣傪寁嶼)


>s
(嬌抣揰偺岓曗傪昞帵)


拲堄丂extrema(嬌抣傪媮傔偨偄娭悢丄惂栺忦審丄曄悢丄's')偺宍偱擖椡偟傑偡丅
弌椡寢壥偼儔僌儔儞僕儏偺忔悢朄傪梡偄偰寁嶼偝傟偰偍傝丄嬌抣揰偺岓曗偼s偵擖傟傜傟偰偄傑偡丅

丂摍埵廤崌倗(x,y)=1偺嬤朤忋偱偺丂z=f(x,y)偺僌儔僼傪昞帵偟偰丄忋偱摼偨寢壥偺徻嵶傪挷傋偰傒傑偟傚偆丅

>plot3d(piecewise(x2+y2/4>0.9 and x2+y2/4<1.1 , x*y,none), x=-2..2,y=-2..2,grid=[100,100])


拲堄丂娭悢f(x,y)=piecewise(忦審丄a(x,y),b(x,y))偼



偲偄偆娭悢傪昞偟傑偡丅

幚廗19.1丂娭悢f(x,y)=e-(x+y-2)2偲g(x,y)=x3-3xy+y3偵偮偄偰丄埲壓偺栤偄偵摎偊側偝偄丅
(1) 忦審g(x,y)=0 偺壓偱偺f(x,y)偺嬌抣傪媮傔側偝偄丅
(2) 忦審f(x,y)=1 偺壓偱偺g(x,y)偺嬌抣傪媮傔側偝偄丅

[惓夝椺]