Question Number 131734 by LYKA last updated on 07/Feb/21
$$\boldsymbol{{given}}\:\boldsymbol{{the}}\:\boldsymbol{{function}} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)=\boldsymbol{{xy}}\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{y}}−\mathrm{1}\right) \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)\:\boldsymbol{{has}}\:\boldsymbol{{some}}\:\left(\mathrm{0},\mathrm{1}\right) \\ $$$$\boldsymbol{{as}}\:\boldsymbol{{a}}\:\boldsymbol{{stationery}}\:\boldsymbol{{point}} \\ $$$$ \\ $$$$\boldsymbol{{use}}\:\boldsymbol{{tylor}}\:\boldsymbol{{series}}\:\boldsymbol{{method}}\:\boldsymbol{{to}}\: \\ $$$$\boldsymbol{{determine}}\:\boldsymbol{{whether}}\:\left(\mathrm{0}.\mathrm{1}\right)\:\boldsymbol{{is}}\:\boldsymbol{{a}} \\ $$$$\boldsymbol{{minima}}\:,\boldsymbol{{maxima}}\:\boldsymbol{{or}}\:\boldsymbol{{saddle}}\: \\ $$$$\boldsymbol{{point}} \\ $$
Answered by guyyy last updated on 11/Feb/21
