# How to distinguish between global maxima/minima and local maxima/minima of a function?

How to distinguish between global maxima/minima and local maxima/minima of a function (when the graph is not provided)?

For instance:I find all the points having f'(x)=0 and do second derivative test.But after that suppose the values are such that it will be a tedious job to individually find and compare the extrema values.Is there any other method?

Can someone provide me with few examples? Even a link will do. (Agreed my question is "broad")

There are a number of inequalities, such as the AM/GM inequality, and Jensen's inequality, which achieve equality only at specific values of the variables, often when they are all equal. When one of these inequalities can be applied, it gives the absolute maximum or minimum, without any need to worry about relative maxima or minima. Often some ingenuity is needed to get the problem into the necessary form.

You can use your first derivative expression to find what the critical point is.

It is called the first-derivative test.

i)If its an inflection point, the sign of derivative does not change across the point

ii)If its a point of minima, the sign changes from-ve to +ve

iii)If its a point of maxima, the sign changes from +ve to -ve

Note: This does not work for discontinuous functions.