i am struggling with the concept of optimization. does anyone have any hints on how to solve these problems???

Answer 1

a function is maximum or minimum only if its derivative is zero (the slope is zero at the top of a mountain or the bottom of a valley.
Of course the converse is not necessarily true. If the slope is zero it is not necessarily a top or a bottom. It could be a pause in descent or ascent. the second derivative will tell you. If the second is +, that is a valley. If the second is minus, that is a peak, if zero, just an inflection point (pause.
Now if you are doing linear programming, that is a different subject and post a problem.