Difference between relative and absolute extremum?

If you're using calculus there really isn't too much of a difference. Now when we are not restricting our range our global or absolute extrema may very well be infinity.

But really, take the first derivative, set it to zero and you will find your extrema. Not sure that this helps but I hope it sheds some light on things for you.

Absolute potential this is the optimal/lowest element to the entire function. working example y=x^2 has an absolute minimum at (0,0). The graph by no potential dips decrease than the x-axis, the variety is [0, infinity) A relative max/min is whilst there's a turning element that's no longer an end of the function's variety.

for relative extremum, we are only looking at neighborhoods, i.e. areas just nearby, and for absolute, it is the entire area in question (your whole domain)

to find relative extrema, you just look for critical values (zeros of derivatives) and use the second derivative test (you should know how to do this) to see if its a max or min

to find absolute extrema, you have to do two things: first, find the biggest (most positive of the local maxes or most negative of the local mins) and that is one candidate. next, you must look for vertical asymptotes on your domain to see if the function shoots to infinity (or negative infinity) in which case you don't have any absolute max (or min). finally, you have to check end behavior - if the function calms down to some constant or zero as x gets really big or small, or it just stays within some range (like sin(x) stays within +/-1 over all real numbers), then one of the earlier checks will have found your max/min. if it goes to infinity or negative infinity (like a polynomial), then you don't have a max or min.