函数f(x)=ax+1/x+2在(-2,正无穷大)为增,求a的值

问题描述:

函数f(x)=ax+1/x+2在(-2,正无穷大)为增,求a的值

f(x) = (ax+1)/(x+2) = (ax+2a-2a+1)/(x+2) = a-(2a-1)/(x+2)x>-2时,x+2单调增,1/(x-2)单调减又:f(x) = a-(2a-1)/(x+2)单调增,∴-(2a-1)/(x+2)单调增,∴(2a-1)/(x+2)单调减∴2a-1>0∴a>1/2...