Expression 23: StartFraction, "y" minus "f" left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis Over "x" minus "x" Subscript, 0 , Baseline , EndFraction equals "f" prime left parenthesis, "x" Subscript, 0 , Baseline , right parenthesisy−fx0x−x0=f′x0
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Expression 24: "y" minus "f" left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis equals "f" prime left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis left parenthesis, "x" minus "x" Subscript, 0 , Baseline , right parenthesisy−fx0=f′x0x−x0
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Expression 25: "y" equals "f" prime left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis left parenthesis, "x" minus "x" Subscript, 0 , Baseline , right parenthesis plus "f" left parenthesis, "x" Subscript, 0 , Baseline , right parenthesisy=f′x0x−x0+fx0
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Expression 26: "y" equals "f" prime left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis "x" minus "f" prime left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis "x" Subscript, 0 , Baseline plus "y" Subscript, 0 , Baseliney=f′x0x−f′x0x0+y0
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Expression 27: "y" equals 7 "x" minus 7 times left parenthesis, negative 2 , right parenthesis minus 3y=7x−7·−2−3
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Expression 28: "y" equals 7 "x" plus 11y=7x+11
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Opgave (eksempel)
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29
Hvor mange tangenter
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med hældningen 0 kan
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grafen for f have?
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Ligningen f ' ( x ) = 0 løses:
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Expression 34: 3 quarters "x" squared minus 2 "x" equals 034x2−2x=0
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Expression 35: "x" Subscript, 1 , Baseline equals StartFraction, negative left parenthesis, negative 2 , right parenthesis minus StartRoot, left parenthesis, negative 2 , right parenthesis squared minus 4 left parenthesis, 3 quarters , right parenthesis times 0 , EndRoot Over 2 left parenthesis, 3 quarters , right parenthesis , EndFractionx1=−−2−−22−434·0234
equals=
00
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Expression 36: "x" Subscript, 2 , Baseline equals StartFraction, negative left parenthesis, negative 2 , right parenthesis plus StartRoot, left parenthesis, negative 2 , right parenthesis squared minus 4 left parenthesis, 3 quarters , right parenthesis times 0 , EndRoot Over 2 left parenthesis, 3 quarters , right parenthesis , EndFractionx2=−−2+−22−434·0234
equals=
2.6 6 6 6 6 6 6 6 6 6 72.66666666667
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Da vi får to løsninger, har f to
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tangenter med hældningen 0.
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Tangenterne er givet ved:
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Expression 40: "y" equals "f" left parenthesis, "x" Subscript, 1 , Baseline , right parenthesisy=fx1
equals=
33
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Expression 41: "y" equals "f" left parenthesis, "x" Subscript, 2 , Baseline , right parenthesisy=fx2
equals=
0.6 2 9 6 2 9 6 2 9 6 30.62962962963
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Punkter
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42
50
powered by
powered by
Start black, left parenthesis, "x" Subscript, 0 , Baseline , "y" Subscript, 0 , Baseline , right parenthesis equals ( negative 2 ; negative 3 ) End blackx0,y0=(−2;−3)
left parenthesis, "x" Subscript, 1 , Baseline , "f" left parenthesis, "x" Subscript, 1 , Baseline , right parenthesis , right parenthesis equals ( 0 ; 3 )x1,fx1=(0;3)
left parenthesis, "x" Subscript, 2 , Baseline , "f" left parenthesis, "x" Subscript, 2 , Baseline , right parenthesis , right parenthesis equals ( 2.6 6 6 6 6 7 ; 0.6 2 9 6 3 )x2,fx2=(2.666667;0.62963)