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Theoretically speaking, it is generally wrong to say that the second derivative is zero, but that the second derivative changes sign on both sides of a point, then this point is the inflection point. If the second derivative is continuous, of course, it can be deduced that the second derivative of this point is 0, because the left and right signs are different. But if the second derivative is allowed to be discontinuous, you can construct a point with no value, which can also be called an inflection point as long as both sides change signs.

Derivatives of second order and above are collectively called higher order derivatives, which are gradually defined by induction. To get the higher derivative, we only need to repeatedly apply the method of getting the first derivative. Taking the second derivative as an example, the derivative f'(X) of the function y=f(x) is generally a function of x, and the second derivative of f'(X) is called the second derivative of f(x), which is denoted as f "(r), y". Derivatives of second order and above are collectively called higher order derivatives.

When the original function of a higher derivative is an even function, its first derivative is odd function, its second derivative is an even function, and its third derivative is odd function. By analogy, it can be concluded that the 2k derivative is an even function and the 2k+ 1 derivative is a odd function. When the original function is odd function, its first derivative is even, its second derivative is odd function and its third derivative is even. By analogy, we can get that 2k derivatives are all odd function.

Derivative, also called derivative function value. Also known as WeChat quotient, it is an important basic concept in calculus. When the independent variable x of the function y=f(x) produces an increment x at point x0, if x approaches 0, there is a limit a in the ratio of the increment y of the output value of the function to the increment x of the independent variable, then A is the derivative at x0, which is denoted as f'(x0) or df(x0)/dx.

/kloc-the development of productivity in the 0/7th century promoted the development of natural science and technology. On the basis of predecessors' creative research, great mathematicians Newton and Leibniz began to study calculus systematically from different angles. Newton's calculus theory is called "flow number". He called the variable flow and the rate of change of the variable flow number, which is equivalent to what we call derivative.