F(x)=2^x+a*2^(2x)=2^x+a*(2^x)^2, 令2^x=t ï¼
æ以 F(x)=G(t)=a*t^2+t =a(x+1/(2a))^2-1/(4a), 顶ç¹å¨(-1/(2a),-1/(4a)),
å 为x<=0,æ以 0<t<=1,
å½a>0æ¶ï¼å¼å£åä¸ä¸
对称轴t=-1/(2a)å¨y轴左边ï¼æ以G(t)å¨(0,1]ä¸åè°éå¢
æ大å¼=G(1)=a+1
å½a=0æ¶ï¼G(t)=t, å¨(0,1]ä¸åè°éå¢ï¼æ大å¼=G(1)=1
å½a<0æ¶,å¼å£åä¸ï¼å¯¹ç§°è½´å¨yè½´å³è¾¹
å½-1/(2a)<=1æ¶ï¼å¯¹ç§°è½´å¨åºé´(0,1]å
ï¼
æ大å¼=G(-1/(2a))= -1/(4a)
å½-1/(2a)>1æ¶ï¼å¯¹ç§°è½´å¨åºé´(0,1]çå³è¾¹ï¼æ以å½æ°å¨(0,1]ä¸åè°éå¢
æ大å¼=G(1)=a+1