Hey Juliana,
To find a point of inflection for a function f(x):
1. Solve f'(x) = 0 for x
This gives you the stationary points (point of inflection, local maximums, and/or local minimums)
2. Now we need to figure out what type of stationary point it is. Around a local minimum, the graph goes down then up. So we have: f'(x)<0 on the left, f'(x) = 0 at the centre, f'(x)>0 on the right.
Around a point of inflection we have f'(x)>0 on both sides of f'(x) = 0 or f'(x)<0 on both sides of f'(x)
I'll leave it to you to see what the "rule" is for a local max but if you don't get it feel free to ask
The above info means that we can test the nature of a stationary point by finding f'(x) a little to the left & a little to the right of the x value you found in part 1.
Let me know if this is unclear
(Note: I did VCE not HSC so I'm unsure if this method is part of your curriculm)