For example, when we want to study some properties of f(X) (range, monotonicity, maximum, minimum, etc. ), we need the monotonicity of f(X).

It is very easy if f(X) is a quadratic function, but what if f(X) is cubic or even quartic, even an exponential and logarithmic function?

We write the domain of f(X) first, then find the derivative f'(X) of f(X), and then calculate some roots of f' (x), which divide the domain into several parts (-3 and 1 in the table), and then we can know the positive and negative of the derivative f' (x) in these intervals.

If the derivative is positive, the monotonicity of the original function f(X) will increase in this interval, and vice versa. This method can be used to study the properties of functions. I wish you a happy study!