Where can I find a description of the method for finding the extremum of a function using the quadratic interpolation-extrapolation method?

Question

Mathematics

They gave me a course assignment: to write a program that searches for the extrema of a function by this method. Climbed the entire Internet (at least Russian-speaking). There are descriptions of the interpolation method and there they always look for the minimum of the function. How to find the maximum? I understand that it’s just that something changes in the formula, but what I need is a sensible mathematical description of what and how. And nowhere (except for the book "optimization methods in examples and tasks") there is not a single example on a specific function. And in the book, again, only the search for a minimum and the method is described not quite the same as in the other descriptions. Please help me find a theory on the issue

Answer 1

argmin f(x) = argmax (-f(x)), that is, where the function f(x) has a minimum, there the function -f(x) will have a maximum. So multiply your function by -1, and look for the minimum there in the same way - as a result, you will find its maximum.