MathDB
Trigonometric Inequality

Source: 0

April 21, 2009
inequalitiestrigonometry

Problem Statement

Let x1,x2,,x9 x_{1} ,x_{2} ,\ldots ,x_{9} be real numbers on \left[ \minus{} 1,1\right]. If \sum _{i \equal{} 1}^{9}x_{i}^{3} \equal{} 0, then what is the largest possible value of \sum _{i \equal{} 1}^{9}x_{i}?
<spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 32<spanclass=latexbold>(C)</span> 3<spanclass=latexbold>(D)</span> 92<spanclass=latexbold>(E)</span> None<span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ \frac {3}{2} \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ \frac {9}{2} \qquad<span class='latex-bold'>(E)</span>\ \text{None}