解ï¼1. 设yï¼mx+n/x
x=1æ¶ y=m+n=4 â´
x=2æ¶ y=2m+n/2=5 âµ
â´ *2-âµ å¾ n=2
代å
¥â´ å¾ m=2
æ
y=2x+2/x å x=4æ¶ y=17/2
2 设ç´çº¿ y=x+b(bï¼0) ä¸å¦¨è®¾A(m,3/m ) ä¸ m+3/m=4 m=1or3
m=1, y=3 b=2
m=3,y=1 b=-2 è æ
y=x+2
(1)设y=kx+b,å
âµå½x=20æ¶,y=360;x=25æ¶,y=210.
â´ , 解å¾
â´y=-30x+960(16â¤xâ¤32)
(2)设æ¯ææå¾æ»å©æ¶¦ä¸ºwå
,
å w=(x-16)y=(x-16)(-30x+960)
=-30(x-24)2+ 1920.
âµ-30<0,â´å½x=24æ¶,wææ大å¼.
æ以ï¼è¿ç¹ï¼1ï¼16aï¼å线çæçæ¯f'(1)=-8a+6
å线çå½æ°å¼ä¸º y=(-8a+6)x+24a-6
ä¸y轴交ç¹ï¼0,6) 24a-6=6 a=1/2
(2)f'(x)=x+6/x-5=(x-3)(x-2)/x x>0
0<x<2 æ x>3 f'(x)>0 f(x)æ¯å¢å½æ°
2â¤xâ¤3 f'(x)â¤0 f(x)æ¯åå½æ°
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