The first step is to determine the monotonicity of f(x)
已知,函数f(x)在定义域D上有单调性,则:
The monotonicity of function f(x)+a is the same as f(x)
. When a>0, the monotonicity of function a·f(x) is the same as f(x).
When a<0, the monotonicity of function a·f(x) is the same. Monotonicity is the opposite of f(x)
复合函数f(g(x))的单调性:
The monotonicity of the composite function f(g(x)) conforms to the law of "same increase and different decrease"
The second step is to determine the monotonicity of its derivative function f '(x) and the positive and negative of f '(x)
当f(x)单调递增:
如果f'(x)单调递增,f(x)单调变化越快
如果f'(x)单调递减,f(x)单调变化越慢
当f(x)单调递减:与上述相反