Solution of inflection point: the inflection point of y=f(x): find f' (x); Let f'(x)=0, find the real root of the equation, and find f'(x) in the interval i.
1, inflection point and extreme point are usually different, and their definitions are different. The first derivative of the extreme point is 0, which describes the increase or decrease of the original function. The second derivative at the inflection point is 0, which describes the concavity and convexity of the original function.
2. Different ways of interpretation. If the function has first, second and third derivatives at this point and its domain, then the point where the first derivative of the function is 0 and the second derivative is not 0 is the extreme point; The point where the second derivative of the function is 0 and the third derivative is not 0 is the inflection point. For example, y = x 4 and x=0 are extreme points rather than inflection points. If there is no derivative at this time, actual judgment is needed. For example, y = | x | x=0, the derivative does not exist, but x = 0 is the minimum point of the function.
Brief introduction of inflection point:
The inflection point, also known as the inflection point, mathematically refers to the point where the sun changes the upward or downward direction of the curve. Intuitively speaking, the inflection point is the point where the tangent intersects the curve (that is, the boundary point between the concave arc and the convex arc of a continuous curve). If the function or chain of the graph has a second derivative at the inflection point, the second derivative has a different sign (from positive to negative or from negative to positive) or does not exist at the inflection point.
The difference between inflection point and extreme point: inflection point is the concave-convex boundary point of function, and the necessary condition for the existence of inflection point is that its second derivative is 0. For a univariate cubic function, there are 1 inflection points, at most there may be two extreme points and at most there may be two stagnation points. In your topic, there is an inflection point, but because the first derivative is always greater than 0 (belonging to increasing function), there is no extreme point and stagnation point. If the coefficient of the cubic term is 0.000 1, there are two extreme points, two stagnation points and 1 inflection points.