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Mathematics-Online problems:

Interactive Problem 61: Parallelogram Formed by Tangent Lines

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
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.)


   

(From: Day of Mathematics 1995)

see also:

  automatically generated: 8/11/2017