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Funktionsundersøgelse

Funktionsundersøgelse. Indhold. Formål Gennemgang af eksempel 7 punkter ø1 side 71 a) f(x)=x 3 -2x 2 -4x+8. Definitionsmængde for f. X-værdier Dm(f) = R. Skæringspunkter med førsteaksen. Nulpunkter f(x)=x 3 -2x 2 -4x+8 L={-2;2} Udregning. Udregning. a 3 =1 a 0 =8.

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Funktionsundersøgelse

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  1. Funktionsundersøgelse

  2. Indhold • Formål • Gennemgang af eksempel 7 punkter ø1 side 71 a) f(x)=x3-2x2-4x+8

  3. Definitionsmængde for f • X-værdier Dm(f) = R

  4. Skæringspunkter med førsteaksen • Nulpunkter f(x)=x3-2x2-4x+8 L={-2;2} Udregning

  5. Udregning a3=1 a0=8 x=1 x=2 x=4 x=8 x=-1 x=-2 x=-4 x=-8 (X3-2x2-4x+8) : (x-2) = x2-4 -(x3-2x2) 0-4x+8 -(-4x+8) 0

  6. -2 2 -2 2 + + - Fortegnsvariation for f • Fortegn for f(x) Fortegnsvariation

  7. Fortegnsvariation

  8. Monotoniforhold for f • Tangenthældningen f ’(x)=3x2-4x-4 • Nulpunkter Udregning L={-0,667;2} • Fortegnsvariation Monotoniforhold x f ’(x) f(x) -0,667 2 + 0 - 0 + Ekstrema for f

  9. Udregning f ’(x)=3x2-4x-4 a=2 b=-4 c=-4 d=b2-4ac d=42-4·3·(-4)=64

  10. Monotoniforhold

  11. Ekstrema for f + 0 - maksimum • 0 + minimum Monotoniforhold for f Lokalt minimum f(-0,667)=9,4814815 (-0,667;9,481) Lokalt maksimum f(2)=0 (2;0)

  12. Værdimængde for f • Y-værdier Vm(f) = R

  13. Tegning

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