函數(shù)f(x)=x^2-8lnx,g(x)=-x^2+14x,若函數(shù)f(x)與g(x)在區(qū)間(a,a+1)上均為增函數(shù),求a的取值范圍.
函數(shù)f(x)=x^2-8lnx,g(x)=-x^2+14x,若函數(shù)f(x)與g(x)在區(qū)間(a,a+1)上均為增函數(shù),求a的取值范圍.
優(yōu)質(zhì)解答
fx=x^2-8lnx,f '(x)=2x-8/x=2(x-4/x)
gx=-x^2+14x g '(x)= -2x+14=2(-x+7)
若函數(shù)fx與gx在區(qū)間(a,a+1)上均為增函數(shù)
則f '(x)=2x-8/x=2(x-4/x)>0
x>4/x
或者x>2;
或者-2x不是應(yīng)該大于0嗎lnx-2