-
ãã®ãšã, a=
3 極å€ã®æ¡ä»¶ããæ±ãã
(ã¢) 3æ¬¡é¢æ°f(x)=23+ar2+bx+cã¯x=1ã§æ¥µå€§å€6ããšã,r=2ã§æ¥µå°å€ããšããšããã
=,b=,c= ã§ãã. ãŸã, f(x) ã®æ¥µå°å€ã¯
â¡ã§ããã
(倧éªç£å€§)
(ã€) f(x)=x-3ar2+3bx ã«ã€ããŠã 次ã®åãã«çãã.
(1) f(x) ãæ¥µå€ãæã€æ¡ä»¶ãα, b ã§è¡šã.
(2) f(x)ã®æ¥µå€§å€ã𿥵å°å€ã®å·®ã4ãšãªãããã®æ¡ä»¶ã a, b ã§è¡šã.
(éŽé¹¿å»çç§åŠå€§)
f'(x) ã䞻圹ã«ãã
f(x) ã3æ¬¡é¢æ°ã®ãšã, f (x)ã¯2æ¬¡é¢æ°ã«ãªã, 極å€ããšãã§ã®å€ã
1,2ãšäžãããããš,'(1)=f(2) = 0 ãšãªãã®ã§ãf'(x)ã¯ã»ãšãã©æ±ºãŸã£ãŠããŸã.
f(x)=2x+a2+bx+c ã®æªç¥æ°a, b, c ã«ã€ããŠã®é¢ä¿åŒãç«ãŠãŠ a, b, c ãæ±ããããããf'(x)
ãæ±ãã«ãã£ãæ¹ãæéãã.
3æ¬¡é¢æ°ã®æ¥µå€ã®å·®ã¯å°é¢æ°ã®å®ç©åã§
f'(x) =0ã®è§£ãα, β (α <β) ãšãããš
f(x)=a(x-a)(z-B)ãšããã.ãŸã, 極å€ã®å·®ã¯,f(a)-f(B)=fff'(x) dr ã§ãã.ãããš
ããããš,å®ç©åã®å
¬åŒâ«(ãšãŒÎ±) (1-B) dr=-1/2 (B-α)ãçšããããšãã§ããŠèšç®ã楜ã«ãªã.
(2)ã¯å€ååŒ]
è§£ç
18
(ã¢) f(x) = 2x3+ax2+bx+c...... â f'(x)=6x2+2ax+b...... â¡
f(x)ã¯x=1, 2ã§æ¥µå€ããšãããã (x)=0ã®è§£ãx=1,2ãšãªã,
f'(x) ã¯, (x-1)(x-2)ã§å²ãåããã â¡ã§2次ã®ä¿æ°ã6ã§ããããšãã
f'(x) =6(x-1)(x-2)=6x²-18x+12
å æ°å®ç
â¡ãã 2a=-18, 6=12
. α=-9, b=12
zat4a-46
zat 2/a-b
f(x)=2x3-9x2+12x+c
2
2
f(1) =6ãã, 2-9+12+c=6 .. c=1
極å°å€ã¯, f (2) =2ã»23-9ã»22+12ã»2+1=5
(ã€) (1) f'(x)=3(2-2ax+b) f'(x) =0ãçžç°ãªã2å®è§£ãæã€ã
ãšãæ¡ä»¶ã§, å€å¥åŒD>0. ã€ãŸããα-60
(2) f(x) =0ãè§£ããŠ,r=a±âd-ba=a-
a=a-ââa²-b, B=a+âa²-b
ãšãããš, f'(x)ã®xã®ä¿æ°ã3ã§ãããã, f'(x) =3(x-α)(x-β)
f(a)-f(B)=f(x)dx=â«3(ãšãŒÎ±)(ãšãŒB)dr=2 (α-B)3
f(a)--
SS f(B)
N
|y=f(x)
if(a)>f(B)
>>⪲ (x-a) (xâB) dx
â¬( 9 âzº / )v=e( 9⿺ (2) ² =¢( 0-8)=
極å€ã®å·®ã4ã§ãããã, 4(â2-634 S .. α-b=1
[6åã®1å
¬åŒ]