[Urgent Question] High school mathematics: When the derivative image is transformed into the original function image, there are two methods to draw the increasing interval and decreasing interval (two convex and two convex respectively). Why? ... Generally, the second derivative is obtained, that is, the derivative of f'(x).

1. If the second derivative f "(x) >; 0, then f'(x) is increasing function, and f(x) is drawn as convex (or concave), such as f(x)=x? ，f'(x)=2x，f ' '(x)= 2 & gt； 0,

So f(x)=x? Is a lower convex function.

2. Similarly, if the second derivative f "(x)

Note: convexity and convexity have nothing to do with the increase or decrease of the original function, and the boundary point between convexity and convexity is the inflection point of the function.

For example, f(x)=x? ，f'(x)=3x？ , f''(x)=6x, let f''(x)=0, x=0,

When x>0 and f''(x)>0, f(x) is convex; When x

F(x) is increasing in R, which shows that convexity and convexity have nothing to do with the increase or decrease of the original function.