Exam confusing?

[MathMethodsGuru]

Hey ATARNotes,

This might be a really simple question, but, I do not really understand what this mean and I keep on seeing it pop up on question typically involve tangents, derivatives and stationary points where you have something like, f(a, f(a)).

What does this actually mean, when you have something lie find:
question: find a, f(a, f(a)).

[S_R_K]

Can you quote a particular question you have in mind? The example you have given doesn't quite make sense.

If the question is about the meaning of "(a, f(a))", then this refers to a coordinate pair where x = a, and y = f(a).

[MathMethodsGuru]

Yeah mate, Heffernan 2017 trial exam:

[MathMethodsGuru]

Forgot part a and b of the question.

[Lear]

Typically exams give you a point (a,f(a)) where they want you to find the nature of stationary point/derivative/tangent/normal in terms of a. You don’t know a (yet) and they often use this step for later questions. It’s simply an expression for a point on f(x) which is represented as a pronumeral.

[MathMethodsGuru]

Ah, thank you for breaking the math jargon down in simpler expression.

Thank you.

[MathMethodsGuru]

for part c, they used the second derivative. Why? Is it do with the point of inflection?

[S_R_K]

for part c, they used the second derivative. Why? Is it do with the point of inflection?

Yes. If (a, f(a)) is a point of inflection, then the second derivative = 0. This is not required knowledge for methods, however (it's specialist content).

What you should know for Methods is that there is exactly one point where f'(x) = a has one solution, and this is where the derivative is at a maximum / minimum (ie. it is a point of inflection). If the cubic has two turning points, this point is halfway between the turning points.