What is an infection point?

Inflective point is an important concept in differential numbers. At the moment of inflection, the function of the function changes its concave - in other words, it changes from the negative to positive curvature or vice versa. This point can be defined or visualized in different ways. In applications in the real world where the system is modeled by a curve, finding an inflexive point is often critical in anticipating the behavior of the system. In any given function, the value of X or the value that is input to the equation, the output represented by the value, produces these values ​​formed by the curve. The concave area up appears on the chart when a bowl -like curve opens up while the concave area down opens. The point at which this concave changes is an infection point.

There are several different methods that can be useful in visualization where the infection point lies on the curve. If one had to place a point on a curve with a straight line stretched through it that only touches the curve - tangent - and triggers this point forl curves, there would be an inflexive point at the exact point where the tangen line intersects over the curve.

mathematically, the point of inflexion is the point where the sign of the second derivative changes. The first derivative of the function measures the speed change speed, as its input changes, and the second derivative measures how this rate itself can change. For example, the speed of the car at a given moment is represented by the first derivative, but its acceleration - increasing or reducing speed - is represented by a second derivative. If the car accelerates, its second derivative is positive, but when it stops accelerating and slows down, its acceleration and the second derivative become negative. This is the point of inflection.

To visualize this graphic visualization, it is important to realize that the concave of the function of the function is expressed by its second derivative. The positive second derivative indicates the concave curve up and the negative second derivative shows the curve that KTErá is concave down. It is difficult to determine the exact point of the inflexion on the chart, so for applications where it is necessary to know its exact value, the inflexic point can be solved for mathematically.

One of the methods of finding an infection point is to take your second derivative, set it straight zero and solve it for x. Not every zero value in this method will be an inflex point, so it is necessary to test the values ​​on the double -page x = 0 to ensure that the second derivative sign actually changes. If so, the value in x is an infection point.