First off, let me say I know these problems can be solved with derivitives in calculus, but that's not what I'm after here.
What is the minimum value of the function f(x) = x^2 - 1?
I know the answer is is -1, but would constructing tables such as the one below be able to reliably bring me to the right answer for problems like this one? If yes, please elaborate the method you'd use when making these tables. I found this on the internet, but can't remember how this works from my Algebra 2 class which was years ago.
We wish to find the mininmum of a quadtratic objective function:
(we can work with monic quadratics as the objective:
has its minima/maxima at the same point as:
If we complete the square we have:
As this obviously has a minimum when which is when
Now you can adapt this to say has a relative max or min at c.
Then observing slopes on yoru interval (a,b) you can get a good estimate of your max or min,
This is just an approximatino of course, but it might be helpful if you are in a sticky situation