Hi guys! Need your help to find roots or compare with zero!

Given derivative of a function:

R^2*(4*R*(1+tan(x)^2)/h/(1-4*R^2*tan(x)^2/h^2)^(1/2)-4*cos(2*acos(2*R*tan(x)/h))*R*(1+tan(x)^2)/h/(1-4*R^2*tan(x)^2/h^2)^(1/2))/cos(x)+R^2*(pi-2*acos(2*R*tan(x)/h)+sin(2*acos(2*R*tan(x)/h)))/cos(x)^2*sin(x) (here R,h-const)

Weeeeeeell,, I need to find X when it is equal to 0; if it is not,, then I'd like to know if the function is incresing or decreasing by comparing with zero. Looking forward your ideas! Thanks a lot! :) aah, by the way,, can somebody teach me to find roots,, to compare ,, etc in Matlab.. Plz.. will be really glad! :D,, thanks for attention**

Answer 1

[Walter Roberson]

You cannot find the zeros of a function given only the derivative of the function. Taking the derivative of a function removes the constant term, but the constant term is essential for finding the zeros of the function. For example, exp(x)-1 has a solution at x = 0, but if you lose the constant term and are dealing with just exp(x) then the only real solution for it is x = -infinity, which is very far away from x = 0.

You can find the zeros of a polynomial using the roots() function.

It is not possible to find the zeros of arbitrary functions: if you could do that, then you could contradict the Turing Incompleteness Theorem (amongst others.)

There are a number of routines that can be used to try to find zeros of an arbitrary function: see for example fzero()