Let $n$ be a non-zero natural number. Can there be equality in the inequality $$\left\|P'\right\|_{L^\infty([-1,1])} \leqslant n^2 \|P\|_{L^\infty([-1,1])}?$$
Let $n$ be a non-zero natural number. Can there be equality in the inequality
$$\left\|P'\right\|_{L^\infty([-1,1])} \leqslant n^2 \|P\|_{L^\infty([-1,1])}?$$