First, we need to understand what derivative is. Derivative is the tangent slope of a function at a certain point, which reflects the rate of change of the function at that point. If the derivative of a function at a certain point is 0, then this point may be the extreme point of the function.
Then, we need to know how to use the derivative to solve the extreme value of the function. Generally speaking, we can solve it by the following steps:
1. Find the derivative of the function. This usually requires derivative rules used in calculus, such as chain rules, product rules and quotient rules.
2. Find the points whose derivatives are 0. These points are called critical points. At these critical points, the function may get the maximum or minimum.
3. Judge each critical point. If the derivative is greater than 0 in the left neighborhood and less than 0 in the right neighborhood of the critical point, then this critical point is the maximum point of the function; Conversely, if the derivative is less than 0 in the left neighborhood of the critical point and greater than 0 in the right neighborhood, then this critical point is the minimum point of the function.
4. If the derivative sign of the neighborhood around the critical point is the same, then the critical point is not the extreme point of the function.
Through the above steps, we can use the derivative to solve the extreme value problem of the function. It should be noted that this method can only solve local extremum, but not global extremum. If we need to solve the global extremum, we need to use other mathematical methods, such as variational method.