I know how local & absolute maxima or minima are calculated, but I don't understand that if we differentiate a function once & put it equal to zero, we get $1,2$ or any other limited number of points of maxima or minima.
But as we all know that there are many local maxima/minima & at each one of them, the slope of function changes its sign(from + to - or converse), so it's value become zero at them. Then why is it that the first derivative equation gives us only few of them? I mean if slope is zero at all of them, then they must all satisfy the equation (I know that the number of roots given by first derivative equation would depend on it being quadratic or cubic or of whatever degree it is, and this makes it even more ambiguous to me).
I know it may sound absurd to some, but I am just a beginner at calculus and have searched quite many places on the web but found nothing. Please help!
We can get as many (local) maxima and minima as we want - the number is not limited. Consider $\sin x$ on $\mathbb{R}$. It has infinitely many maxima and minima (and at all of them the derivative, $\cos x$, is zero).