how to prove that : $\displaystyle \noindent\(|x^3-p^3|\leq \ 7p^2 |x-p| \ if \noindent\ |x|\leq |2p| $
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Originally Posted by Berge how to prove that : $\displaystyle \noindent\(|x^3-p^3|\leq \ 7p^2 |x-p| \ if \noindent\ |x|\leq |2p|$ Recall that $\displaystyle x^3-p^3=(x-p)(x^2+xp+p^2)$ So $\displaystyle |x^2+xp+p^2|\le x^2+|x||p|+p^2$ Show us what you can do with that.
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