How do I calculate extreme points?

To calculate an extreme point, you need extreme points

Two values, each on the X and Y axes of a graph, are generally referred to as extreme points. How to use these two values ​​in the Curve discussion can be calculated in this manual. A definition of what an extreme point, an extreme point and an extreme value are is necessary before you can actually start the calculation.

• In colloquial usage, extreme points are referred to as one value on the X and one on the Y axis. However, you have to go a little more precisely here and clearly differentiate the terms. The said X value actually represents the extreme point. The Y value, on the other hand, is called the extreme value.
• Extreme points are calculated in the curve discussion. This is either the highest (maximum) or the lowest (minimum) value in a given environment on a graph. An extreme point consists of an extreme value and an extreme point.
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• If the maximum is the highest point in its interval, and only there, then it is called the relative maximum. The term local maximum can also be used. A minimum is the local minimum if it is the lowest point in its interval.
• In the event that a maximum or minimum is the highest or lowest point in the entire function, these are referred to as the global maximum or minimum.


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How to calculate extreme points of a function graph

1. In order to calculate an extreme point, you should first think about when a point becomes an extreme point. As a rule of thumb, one can say that the point at which a graph no longer rises is the maximum. From this point on, the graph only falls and the point at which it is lowest and then rises again is the minimum according to the rule of thumb.
2. Now this consideration must be applied to mathematics. The derivative of the function is positive as long as the function is monotonically increasing. Conversely, the same applies to a monotonically decreasing function. So it is necessary to find the point where the derivative changes from positive to negative. This is the zero of the derivative. This represents the necessary condition for calculating the extreme points. However, it can only be decided later whether it is actually a maximum or a minimum
3. First, you need to derive the function and set it equal to zero. Then you will get the necessary condition. Take the following function as an example: f (x) = 1 / 9x³ - 1 / 3x² - 8 / 3x + 26/9. This function is now derived as follows: f '(x) = 1 / 3x²-2 / 3x-8/3.
4. Set this derivative equal to zero in order to obtain the necessary condition, in the example 1 / 3x²-2 / 3x-8/3 = 0. Take the derivative times three to get x²-2x-8 = 0.
5. Plug in the p / q formula and use -2 as p and -8 as q. Example: x1,2 = - -2/2 ± √ (-2/2) ² - (- 8).
6. Solve this for x1.2 in the following calculation steps. Example: x1,2 = 1 ± √9; You get for x1 = -2 and for x2 = 4.
7. Substitute these two x-values ​​into the original function f (x). Under no circumstances may you use the values ​​in the derivative, because only the output function gives you y-values! Then compute the extreme points by adding the Functions calculate with the two x-values ​​and for this example you would have to use the two extreme points E₁ (-2 | 6) and E.₂ (-4 | 6) obtained.

Calculating extreme points requires a certain amount of practice and a certain amount of prior mathematical knowledge. With practice and a lot of patience, you can learn and be in mathematics use.