Question Number 171008 by Mastermind last updated on 06/Jun/22
$${Find}\:{the}\:{maximum}\:{and}\:{minimum} \\ $$$${values}\:{of}\:{h}\left({x}\right)=\frac{\mathrm{4}}{\mathrm{3}}{x}^{\mathrm{3}} +\frac{\mathrm{9}}{\mathrm{2}}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{8}. \\ $$$$ \\ $$$${Mastermind} \\ $$
Commented by mr W last updated on 06/Jun/22
$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}{h}\left({x}\right)=−\infty \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{h}\left({x}\right)=+\infty \\ $$$$\Rightarrow{h}\left({x}\right)\:{has}\:{no}\:{minimum}\:{or}\:{maximum}! \\ $$$${it}\:{can}\:{get}\:{any}\:{value}\:{in}\:\left(−\infty,+\infty\right). \\ $$