By considering $\displaystyle \frac{1}{3}x - x^{\frac{1}{3}} $ or otherwise, show that:

$\displaystyle \sqrt[3]{x} < \frac{1}{3}x + \frac{2}{3}$ for all x with 0 < x < 1.

This is another past paper anaylsis question...just wondering if someone could please tell me what method should be used to do this?! I have no idea! Possibly Taylor series?

Thanks in advance!