Question Number 7766 by 314159 last updated on 14/Sep/16
Commented by sou1618 last updated on 14/Sep/16
$${f}\left({xy}\right)={f}\left({x}\right)+{f}\left({y}\right) \\ $$$${f}\left({e}^{\mathrm{2}} \right)=−\mathrm{8}\:\:\:\:\:\:\:\left({Q}\mathrm{7771}\right) \\ $$$$ \\ $$$${f}''\left(\mathrm{2}\right)=?? \\ $$$$ \\ $$
Commented by Yozzia last updated on 14/Sep/16
$${f}''\left(\mathrm{2}\right)=\mathrm{1}\:?\:{I}'{m}\:{not}\:{sure}\:{if}\:{what}\:{I}\:{tried} \\ $$$${is}\:{wrong}. \\ $$
Commented by Yozzia last updated on 15/Sep/16
$${Let}\:{f}\left({x}\right)=−\mathrm{4}{lnx}\Rightarrow{f}\left({e}^{\mathrm{2}} \right)=−\mathrm{4}×\mathrm{2}=−\mathrm{8} \\ $$$$\Rightarrow{f}'\left({x}\right)=−\mathrm{4}/{x}\Rightarrow{f}''\left({x}\right)=\mathrm{4}/{x}^{\mathrm{2}} \Rightarrow{f}''\left(\mathrm{2}\right)=\mathrm{4}/\mathrm{4}=\mathrm{1} \\ $$
Commented by 314159 last updated on 15/Sep/16
$${Good}! \\ $$