A: The first derivative is the slope of the curve. When the first derivative is greater than 0, it is increasing function. When the first derivative is less than 0, it is a decreasing function, and when the first derivative is equal to 0, the function appears stagnation point. If the time function changes from increasing function stagnation point to decreasing function, the function has a maximum (stagnation point becomes a maximum point); When the function changes from a decreasing function to a increasing function, there is a minimum point (the stagnation point becomes a minimum point); If the function still keeps the original increasing function or subtraction function after the stagnation point, then this is the real inflection point, not the extreme point. But for a complex answer function, we can't describe it with images, and we can't use the first derivative to judge whether it is an extreme point or an inflection point, so we use the second derivative. The second derivative is a function to judge the changing trend of the first derivative; Whether it is acceleration or deceleration (similar to acceleration in physics) can be known by the second derivative. When the second derivative is greater than 0, it means that the operation is accelerated, that is to say, the speed is getting faster and faster, and the function changes faster than the independent variable. The curve is like a cross-sectional view of a bowl standing upright on a horizontal plane, so it has a minimum value. On the contrary. Like the cross section of a bowl buckled on a horizontal surface. So, there is a maximum. If it is equal to 0, it means that there is still no gentle movement of acceleration, no increase or decrease of acceleration, and the direction of the curve has not changed; In other words, this point is not an extreme point, but an inflection point.

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