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$f(x)=\\simplify[all,!collectNumbers,!noleadingminus, fractionNumbers]{{a}x^3+{b}x^2-{c}x+{d}}$

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$f'(x)=$ [[0]]

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Bruk blant annet derivasjonsregelen $(x^n )'=n x^{n-1}$

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Videoen i denne lenken viser et eksempel på derivasjon av en polynomfunksjon.

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Undersøk hvor  $f'(x)$ skifter fortegn, og bestem eventuelle topp- og bunnpunkter:

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Koordinatene til bunnpunktet er: ( [[0]] , [[2]] )

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Koordinatene til toppunktet er: ( [[1]] , [[3]] )

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Når vi deriverer får vi $\\displaystyle f'(x)=\\simplify[std]{{3*a}x^2+{2*b}x-{c}}$.

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For å finne de stasjonære punktene må vi løse  $\\displaystyle f'(x)=0$ for $x$, dvs likningen

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$\\simplify[std]{{3*a}x^2+{2*b}x-{c}=0}$.

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Denne likningen har to løsninger; $x=\\var{r1}$ og $x=-\\var{r2}$. For klassifisere de stasjonære punktene (avgjøre om de er toppunkt, bunnpunkt eller terrassepunkt) kan vi tegne fortegnslinja til den deriverte.  

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Dere kan finne mer hjelp i videosnutten i denne lenken.

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Her skal vi finne koordinatene til funksjonens stasjonære punkter, og avgjøre om de er toppunkter, bunnpunkter eller terrassepunkter.

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Finding the stationary points of a cubic with two turning points

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