Question Number 39170 by Rio Mike last updated on 03/Jul/18
$${Find}\:{the}\:{value}\:{of}\:{k}\:{if}\: \\ $$$$\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\:\mathrm{6}\:{when}\:{x}\:=\:−\mathrm{1}\: \\ $$$${and}\:{f}\left({x}\right)\:=\:\mathrm{3}{x}^{\mathrm{3}} \:−\:{kx}^{\mathrm{2}} \:+\:\mathrm{1}\: \\ $$$${if}\:{f}\left(\mathrm{2}\right)\:=\:\mathrm{8}\:{find}\:{one}\:{factor}\:{of} \\ $$$${f}\left({x}\right)\:{and}\:{hence}\:{Evaluate} \\ $$$$\underset{{x}\rightarrow\infty} {{lim}}\left({f}\left({x}\right)\right). \\ $$