how to calculate relative extrema?



I'm an adult student who's trying to do some homework using Maxima, as I 
cannot afford the time to commute 20km to the university campus to use 
their Maple workstations after work hours.

Several fruitless hours of searching through the documentation and the 
Internet in general has left me very puzzled. Maxima - seemingly - has 
no mechanism for calculating the relative extrema of a polynomial over a 
given range. Other posts implied that a function 'lbfgs' can do this 
function, but the language in the help file for this function seems 
targeted to PhD candidates, as I cannot make heads or tails out of it.

So, experts: say you have a fourth-order function like f(x):=10x^4 - 
3x^3 + 2x^2 -6x + 1. Is there any command for finding the minimum and 
maximum values of this function over a specified range? Is there no 
equivalent to the Maple "maximize" and "minimize" functions? If 'lbfgs' 
is the only way to do so, can someone provide a plain-English 
explanation as to how this function works?

Many thanks,
Adam