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You will find advice for each task in the test.

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

$f'(x)=$ [[0]]

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Use derivation rule $(x^n )'=n x^{n-1}$

Use this link for more information.

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Determine where $f'(x)$ has its maximum- and minimumpoint.

Coordinate for maximumpoint: ( [[0]] , [[2]] )

Coordinate for minimumpoint: ( [[1]] , [[3]] )

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When vi derivate the function, we get $\\displaystyle f'(x)=\\simplify[std]{{3*a}x^2+{2*b}x-{c}}$.

To find the stationary points, we have to solve $\\displaystyle f'(x)=0$ for $x$,

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

This equation has two solutions; $x=\\var{r1}$ og $x=-\\var{r2}$. To classify the stationary points (maximumpoint, minimumpoint or saddle point) we make a sign table for the derivated function.

To find out more, check out this movie:

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Find the coordinates to the functions stationary points and determine if they are maximum points, minimum point og saddle points.

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Finding the stationary points of a cubic with two turning points

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