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Mathematics-Online problems:

Problem of the week


The tangent lines at the extrema of the function

$\displaystyle f(x) = x^3 - 3x
$

intersect the graph of this function at the points $ P$ and $ Q$ once more.
\includegraphics{A364_bild}
Determine the points $ P$ and $ Q.$ Find the equations of the tangent lines $ T_P$ and $ T_Q$ at these points and calculate the area $ A$ of the parallelogram formed by the four tangent lines.


Answer:

$ P$ $ =$ $ \big($ , $ \big)$
$ Q$ $ =$ $ \big($ , $ \big)$
$ T_P$ $ =$ $ \ $$ x\ +$
$ T_Q$ $ =$ $ \ $$ x\ +$
$ A$ $ =$ $ \ $

(The result should be correct to two decimal places.)


   


[solution to the problem of the previous week]