Definition of derivative: The instantaneous change rate of a function at at is called the derivative of the function at AT, and it is recorded as or, that is, if every point of the function has a derivative in the open interval, each of them has a definite derivative at this time, thus forming a new function. This function is called the derivative function of the function in the open interval, or derivative for short.

Derivative function 20 questions

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The application of derivative in studying function 1. Monotonicity and derivative of function;

Generally speaking, the monotonicity of a function has the following relationship with the sign of its derivative: within a certain interval (a, b)

(1) If > 0, the function y=f(x) monotonically increases in this interval;

(2) If < 0, the function y=f(x) monotonically decreases in this interval;

2. Extremes and derivatives of functions:

Extreme value reflects the size of a function near a certain point.

The method of finding the extreme value of the function y=f(x) is as follows:

(1) If the left side is > 0 and the right side is < 0, it is the maximum;

(2) if it is near the left side < 0 and the right side > 0, it is the minimum value;

3. Maximum (minimum) value and derivative of the function:

Find the maximum and minimum values of the function y=f(x) on [a, b]:

(1) Find the extreme value of the function y=f(x) in [a, b];

(2) Compare the extreme value of the function y=f(x) with the function values f(a) and f(b) at the endpoint, where the largest is the maximum value and the smallest is the minimum value.