For part iv, I think that the section of graph to the right of the asymptotic line x = 2a should be below the x-axis, starting out from a low of negative infinity to a value close to zero (i.e. a complete reflection of that portion in the x-axis).

Little bit of contention/issue for the portion between x = 0 and x = 2a as well, in part (iv) .

f'(x) should be decreasing from +∞ to 0 , and from 0 to -∞ at a constant/near constant rate, i.e straight line.

But what is drawn indicates that the rate of decrease of f'(x) is slowing down rather significantly as f'(x) approaches 0 , where the minimum point of f(x) is.

Will have to see the marker's discretion

Anonymous, you can try to plot f(x) = ln(0.04x³ + 0.45x² + 1.5x + 1.75) / (x² - 1.5x) in desmos.com

It will give you a graph that is very close to f(x). Then you can plot f'(x) in the next line to see how it would turn out.

The constants above can be adjusted to get a better fit of the actual f(x).