How to find critical points of a fraction?
We can find critical points of a fraction by solving the equation that defines the fraction. For example, to find the critical points of we solve the equation which yields the solutions and If you want to solve an equation for you use the reciprocal of the denominator and the reciprocal of the numerator
How to find critical points of a rational function with no real roots?
If a fraction has no real roots then the function is a polynomial. Finding the critical points of a polynomial is much easier than the general fraction case. The critical points of a polynomial are the roots of its derivative. These roots can be found with the well-known derivative test. If no roots exist, the function is a local minimum or maximum. If there are multiple roots, then the function has more than one critical point.
How to find critical points of a rational function?
In order to find the critical points of a rational function, you need to find the solutions to the function’s equation, S(x) = 0. You can do this by factoring the function into a product of simpler functions.
How to find critical points of a rational function with complex
It is not easy to find the critical points of a function. The main problem is that the function itself might not be defined at some points. In order to find the critical points, we use the fraction approach. First, we represent the function as a fraction of two polynomials. The fraction is called a fractionization of the original function. If the denominator of the fraction is zero at some point, the fraction has a pole. A pole is also called a singularity. Therefore
How to find critical points of a rational function with no imaginary roots?
A rational function with no imaginary roots has no critical points. A rational function is a quotient of two polynomials. So if it has no imaginary roots, then neither of its numerator or denominator can have an imaginary root either. In other words, the polynomial has no roots with an imaginary coefficient. Let's look at an example: