Hey, looks like I'm stuck again :(

If $\displaystyle -2 <= x <= 1$, use the triangle inequality to show that $\displaystyle |2x^3 - 4x^2 +3x - 1| <=39$

I'm having way too much trouble trying to figure this out!!

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- Sep 24th 2009, 06:41 PMtkdiamond08Triangle Inequality
Hey, looks like I'm stuck again :(

If $\displaystyle -2 <= x <= 1$, use the triangle inequality to show that $\displaystyle |2x^3 - 4x^2 +3x - 1| <=39$

I'm having way too much trouble trying to figure this out!! - Sep 25th 2009, 03:06 AMPlato
$\displaystyle \begin{gathered}

- 2 \leqslant x \leqslant 1\, \Rightarrow \,\left| x \right| \leqslant 2 \hfill \\

\left| {2x^3 - 4x^2 + 3x - 1} \right| \leqslant 2\left| x \right|^3 + 4\left| x \right|^2 + 3\left| x \right| + 1 \hfill \\

\end{gathered} $