how do I even begin to solve this?

You begin by finding where f'(x)=0

>>220566
that's the easiest part, it's at x= 4/3

>>220557
You should start by finding the domain. Since plugging anything into x greater than 2 gives you an imaginary number your domain should be D:(∞,2]. Then you find the critical point with >>220566
.

Figure out if the critical point is a local min or max. With all that info you should have the answers to (i) and (ii).

You start solving (iii) by finding where f''(x)=0.

>>220595
whoops, D:(-∞,2]

>>220595
>>220595
Is this enough or do you need more help?

>>220557
For the sketch, note that f(0) = f(2) = 0.

Also in (ii), don't forget the value at the boundary f(2) = 0 which is also a local minimum.