http://m.imgur.com/a/pb6vO
Is there any real method for determining the shape of these graphs? I can find out the features they will have but don't know what it'll look like altogether.
Q5) Makes a bit of sense but Q6) I knew there would be a negative point of inflection but couldn't of even guessed there would be 2 turning points like that..
You can usually find out most of the information to draw a graph like that, but the stationary points are a bit more difficult. As it's a positive function to the power of 5, it goes up like a (positive) cubic. As it's x^3(x^2-1) then you can find out the x intercepts are 0,-1,1, and since it's x^3(...) then you know there's a point of inflection at that x intercept. From there, you can plot the x intercepts, know the general shape (going up like a cubic) and you know there's a point of inflection at x=0, so from there you can deduce there are two turning points, which you find using your calculator. From left to right, it goes up to the first intercept at x=-1, then goes down the reach the second intercept at x=0 which has a point of inflection, down then back up to reach x=1 and continues upwards.
Hope this helps a little, I'm a bit rusty