Please, can someone give me more information on how to check if points are local or global maximum/minimum. I am aware of the second derivative test of determining the local minimum/maximum. But how do I check for global min/max? An example to illustrate this would be very much appreciated. Thanks.
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A very useful method is Sturm's principle which says that a continuous function on a compact domain (e. g. a closed interval) which is bounded below/above an has at most one local minimum/maximum must have a global minimun/maximum at this very place.
If your function in question, however, has more than one local minimum/maximum, you have to compare the values of the function at all these minima/maxima and those with minimal/maximal value among these candidates are your global minima/maxima.
In each case, you should check first, that your function is bounded below/above!
Thus, for $f:[a,b] \rightarrow \Bbb R$ differentiable, you should proceed as follows: