Question

求证函数f(x)=(3-x)/(4x+1)函数在(-1/4，+∞)上递减，具体过程，万分感谢！！！！

Answer 1

任取x2>x1>-1/4
f(x2)-f(x1)
=(3-x2)/(4x2+1)-(3-x1)/(4x1+1)
=((3-x2)(4x1+1)-(3-x1)(4x2+1))/(4x2+1)(4x1+1)
=(12x1+3-4x1x2-x2-12x2-3+4x1x2+x1)/(4x1+1)(4x2+1)
=13(x1-x2)/(4x1+1)(4x2+1)
x1-x2<0
4x1+1>0,4x2+1>0
f(x2)-ff(x1)<0
f(x2)<f(x1)
所以f（x)在（-1/4,+无穷）单调递减。