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Mathematics-Online problems:

Interactive Problem 861: Area Enclosed by Orthogonal Tangents

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#./interaufg861_en.tex#The figure shows the graph of the polynomial

$\displaystyle p(x)=x^2(a-x^2) $

as well as the tangent lines drawn at the points $ Q_i$ on the curve and thus forming a square.

\includegraphics[width=8.3cm]{TdM_05_A3_bild1.eps}


Answer:

$ P$ = $ \Big($ $ \sqrt a$, $ a^2 \Big)$
$ a$ =      
$ Q_1$ = $ \Big($ , $ \Big)$
$ Q_2$ = $ \Big($ , $ \Big)$
$ A$ =      

(The results should be correct to four decimal places.)


   

(From: Day of Mathematics 2005)
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  automatically generated: 2/ 6/2018