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Mathematics-Online problems:

Interactive Problem 88: Determination of Coefficients of a Polynomial, Extrema, and Area Calculation

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The figure shows the graph of a polynomial $ p(x) = a + bx^2 + cx^4.$

\includegraphics[width=0.7\linewidth]{kurvdiss.eps}

Determine the coefficients $ a, b,$ and $ c.$ Determine also the values of $ x$ for the extrema and the inflection points. Find the area $ A$ of the shaded region.


Answer:

Coefficients: $ a =$ $ b = $ $ c = \quad \,\,$
Extrema: $ x_1 =$ $ x_{2,3} = $ $ \pm$  
Inflection points: $ x_{4,5} =$ $ \pm$      
Area: $ A =$      

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


   

(From: Day of Mathematics 2002)
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  automatically generated: 8/11/2017