Does the tangent of a function being at a maximum necessarily mean that the function itself is at a maximum? I am supposed to find whether del is at a maximum at w = (tansig*taneps)^(-1/2) del = arctan(w*(tsig-teps)/(1+(w^2*(tsig*teps)))) tansig and taneps are constants and w is the independent variable Using MATLAB, I've found that the derivative of tan(del) at the given w is in fact 0, and using a given graph of tan(del), I can see that the only point where the slope of the tangent is 0, is at a maximum peak. And so, I know that tan(del) at the given w is maximum. Knowing this, can I claim that del itself is maximum at the specified w? Thanks you all!