// Numbas version: exam_results_page_options {"name": "Funksjoner og derivasjon 1T", "metadata": {"description": "Tester grunnleggende kunnskaper fra 1T om funksjoner og derivasjon.
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Hei! Lykke til med denne prøven!

\n

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Tips: Når du svarer med en brøk (for eksempel 7/2) må brøken være forkortet. Svaret 14/4 vil ikke bli godkjent.

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Jeg lover å svare på oppgavene uten hjelp fra internet eller andre mennesker.

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Jeg lover å kun bruke skrivesaker, IKKE kalkulator, GeoGebra, eller andre hjelpemidler.

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En rasjonal funksjon er gitt ved

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$ f(x) = \\frac{\\var{a} x + \\var{b}}{ \\var{c} x - \\var{d}}  $

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Svar på forkortet brøkform (\"lowest terms\") i alle oppgavene.

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Verdien f(-2)

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y-verdien til horisontal asymptote

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Finn bruddpunktet til funksjonen.

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Svar med $x$-verdien:

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Finn nullpunktet til funksjonen.

\n

Svar med $x$-verdien:

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Regn ut $f(-2)$.

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Finn den horisontale asymptoten.

\n

Svar med $y$-verdien:

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Funksjonen $f$ er gitt ved $f(x) = \\simplify{ {a}x^2 + {b} x + {c} }$.

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Gjennomsnittlig vekstfart

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Funksjonen har en symmetrilinje. Hva er $x$-verdien til denne symmetrilinjen?

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Hva er gjennomsnittlig vekstfart for funksjonen $f$ fra $x = \\var{x1}$ til $x=\\var{x2}$?

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Hva er den momentane vekstfarten til $f$ for $x= \\var{x1}$?

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Funksjonen $f$ har en tangent for $x = \\var{x1}$. I hvilken $y$-verdi skjærer denne tangenten $y$-aksen?

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Funksjonen $f$ er definert ved $f(x) = \\var{a}x^3 + \\var{b} x^2 + \\var{c} x + \\var{d}$.

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x-verdi til første ekstremalpunkt

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x-verdi til andre ekstremalpunkt

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Tall som bestemmer den ledende koeffisenten (som skal være 2*alpha)

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Konstantledd

", "templateType": "randrange"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "2*alpha", "description": "

Ledende koeffisient

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Andregradskoeffisient

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Førstegradskoeffisient

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Første ekstremalverdi

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Andre ekstremalverdi

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Verdien f(-2)

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Verdien f'(-1)

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Regn ut $f(-2)$.

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Regn ut $f'(-1)$.

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Funksjonen har ett toppunkt og ett bunnpunkt.

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Hva er $x$-verdien til toppunktet?

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Hva er $y$-verdien til toppunktet?

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Hva er $x$-verdien til bunnpunktet?

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Hva er $y$-verdien til bunnpunktet?

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En andregradsfunksjon $f$ er gitt ved $f(x) = a x^2 + b x + c$.

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Du får vite at grafen til $f$ skjærer $y$-aksen i punktet $y=\\var{c}$ og at ekstremalpunktet til $f$ er $(\\var{s}, \\var{ex})$.

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Finn koeffisientene $a$, $b$ og $c$.

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Koeffisienten $a$ er:

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Koeffisienten $b$ er:

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Koeffisienten $c$ er:

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Bare 5 minutter igjen!

"}}, "feedback": {"showactualmark": false, "showtotalmark": true, "showanswerstate": false, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "feedbackmessages": [{"message": "

Bra! Husk nå å ta skjermbilde av resultatet ditt!

", "threshold": "30"}]}, "contributors": [{"name": "Andreas Holmstrom", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/285/"}], "extensions": [], "custom_part_types": [], "resources": []}