Fixed Point Equations - Exam Revision Help

In summary, the person is working on their exam revision and is looking for help with the fixed point equation. They mention that a fixed point is a value that satisfies f(x)=x for a given function and they have a quadratic equation to work with. They express uncertainty but thank the person for their help.
  • #1
morbello
73
0
hi I am working on my exam revision and need to know the fixed point equation.if you could help it would be apreciated.



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  • #2
I have no idea what you mean by the "fixed point equation". A value (number, point, etc.) satifying f(x)= x for a given function is a "fixed point" of that function. That may be the equation you are looking for.
 
  • #3
so to find a fixed point f(x)=x and the numbers found are at there peak or that they are on the y=x axis.ive got a quadratic equation to work from and asked to find the fixed points.im unsure but thank you for your help.
 

1. What are fixed point equations?

Fixed point equations are mathematical equations in which the unknown variable appears both as an argument of a function and as the result of that function. They are used to find the value of the unknown variable that makes the equation true.

2. How do fixed point equations differ from other types of equations?

Unlike other types of equations, fixed point equations do not have a specific algebraic solution. Instead, they are solved iteratively using numerical methods.

3. What are some examples of fixed point equations?

Some examples of fixed point equations include the logistic map, the Newton-Raphson method for finding roots, and the Mandelbrot set. They are used in various fields such as physics, economics, and computer science.

4. How are fixed point equations solved?

Fixed point equations are solved using iterative methods, such as the fixed point iteration method or the bisection method. These methods involve repeatedly plugging in an initial guess for the unknown variable and using the result to refine the guess until the solution is found.

5. How can fixed point equations be applied in real-world situations?

Fixed point equations can be applied in various real-world situations, such as predicting population growth, finding the optimal solution for a business problem, or simulating complex systems. They are also used in numerical analysis and computer graphics.

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