Curve sketching questions that ask for points of inflexion and other calculus stuff will almost always be in separate parts [i.e. part i) and part ii)]. Part i) will usually ask for finding the points of inflexion or stationary points and then part ii) will usually be drawing the actual graph.
In terms of finding points of inflexion, there is no other way to find it without f"(x)=0. This is the reason why questions that involve finding points of inflexion for tricker and longer functions are usually worth 3 marks in Math Ext 1.
For other general tips for curve sketching, just remember to always find the following as a general rule:
- y and x intercepts
- horizontal and vertical asymptotes
- whether the function is even or odd (this can speed up the graphing process)
Tips for finding horizontal asymptotes
- if the highest degree power of the polynomial in the numerator is smaller than the highest degree power of the denominator, then the horizontal asymptote is y=0.
- if the highest degree power of the polynomial in the numerator is equal to to the highest degree power of the denominator, then the horizontal asymptote is y=b/a where 'b' is the coefficient of the highest degree power of the numerator and 'a' is the coefficient of the highest degree power of the denominator.
- if the highest degree power of the polynomial in the numerator is one higher than the highest degree power of the denominator, then there is an oblique asymptote
Eh, hopefully that made sense - it's a bit tricky to explain stuff without diagrams and actual examples lol.
