# Triangle Inequality

• September 24th 2009, 06:41 PM
tkdiamond08
Triangle Inequality
Hey, looks like I'm stuck again :(

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

I'm having way too much trouble trying to figure this out!!
• September 25th 2009, 03:06 AM
Plato
$\begin{gathered}
- 2 \leqslant x \leqslant 1\, \Rightarrow \,\left| x \right| \leqslant 2 \hfill \\
\left| {2x^3 - 4x^2 + 3x - 1} \right| \leqslant 2\left| x \right|^3 + 4\left| x \right|^2 + 3\left| x \right| + 1 \hfill \\
\end{gathered}$