In lectures we did questions like (in the simplest form) f(x,y,z) = x + 2y + z subject to a constraint, eg. x^2 + y^2 + z^2 = 48 Find the critical points, value and determine the max/min
In the exam papers some of the questions have the constraint with <= instead of just =. Does this make a big difference to how I approach the question?
Also, when I get the critical values, how do I determine which points are a max/min? Not specifically the example above but in general.
Lastly does the term "on a closed disk" in place of constraint hold any significance?
Thanks in advance for any help...