The concave-convex boundary point of a curve is called inflection point, also known as inflection point, which refers to the point that changes the upward or downward direction of the curve in mathematics. Intuitively speaking, the inflection point is to let the tangents cross. If the function of the graph has a second derivative at the inflection point, the sign of the second derivative changes from positive to negative, from negative to positive or does not exist at the inflection point.
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If the derivative f' of the differentiable function f rises monotonously in a certain interval, that is, the second derivative exists, then in this interval, the second derivative is greater than zero and f is concave; That is to say, a concave function has a declining slope (where declining only means not rising but strictly falling), which means that it allows the existence of zero slope. )
If the second derivative f'(x) of quadratic differentiable function f is positive (or it has positive acceleration), then its image is concave; If the second derivative f'(x) is negative, the image will be convex. If a certain point changes the convexity of the image, it is an inflection point.