ï¼1ï¼
f(x)=x^2-lnx
f(1)=1-0=1
f'(x)=2x-1/x
å¨ç¹ï¼1,1ï¼å¤çå线æçk=f'(1)=2-1=1
æ²çº¿y=f(x)å¨ç¹ï¼1ï¼f(1)ï¼å¤ç
å线æ¹ç¨ï¼y-1=1(x-1)ï¼å³ï¼y=x
ï¼2ï¼
f'(x)=2x-1/x=(2x^2-1)/x = 2(x+â2/2)(x-â2/2)/x
xâï¼-âï¼-â2/2ï¼åï¼0ï¼â2/2ï¼æ¶ï¼f'(x)ï¼0ï¼f(x)åè°åï¼
xâï¼-â2/2ï¼0ï¼åï¼â2/2ï¼+âï¼æ¶ï¼f'(x)ï¼0ï¼f(x)åè°å¢ã
ï¼3ï¼
g(x)=f(x)-x^2+ax=x^2-lnx-x^2+ax=ax-lnx
g'(x)=a-1/x=(ax-1)/x=a(x-1/a)/x
a>0
xï¼0æxï¼1/aæ¶ï¼åè°å¢ï¼0ï¼xï¼1/aæ¶åè°å
xå±äº(0,e]ï¼g(x)çæå°å¼æ¯3
å¦æ1/aï¼eï¼åå½x=1/aæ¶åæå°å¼ï¼g(1/a)=a*1/a-ln(1/a)=1+lna=3ï¼lna=2ï¼a=e^2
å¦æ1/aï¼eï¼åå½x=eæ¶åæå°å¼ï¼g(e)=a*e-lne=ae-1=3ï¼ae=4ï¼a=4/eï¼ä¸ç¬¦å1/aï¼eçè¦æ±
综ä¸ï¼a=e^2