Second derivative to prove nature of stationary points

[sailinginwater]

Are we allowed to use the second derivative to prove nature of stationary points in the methods exam?

[clovvy]

Are we allowed to use the second derivative to prove nature of stationary points in the methods exam?

Yes, you can either use the second derivative or the table.....

[sailinginwater]

Yes, you can either use the second derivative or the table.....

Do you know if it's the same for vce?

[S200]

I think that the table is required in VCE, 'cause I don't recall learning the \(f^{\prime \prime}(x)\) for any stationary points.

[Sine]

Are we allowed to use the second derivative to prove nature of stationary points in the methods exam?

IMO it's not advised to use the second derivative test in methods since it is not a part of the syllabus - so you can't be sure to get the marks from every single possible assessor. This is because for certain questions their may be specific marks awarded for a gradient sign table and if you don't do a table you can't get those marks (even if the answer is correct).

Other than trying to flex mathematical prowess to your examiner there really is not point since it only saves a little bit of time with the possibility of dropping marks.

Some people will say that an assessor have said it's ok but since there is no consensus between everyone it's much safer to just use the table.

[sailinginwater]

IMO it's not advised to use the second derivative test in methods since it is not a part of the syllabus - so you can't be sure to get the marks from every single possible assessor. This is because for certain questions their may be specific marks awarded for a gradient sign table and if you don't do a table you can't get those marks (even if the answer is correct).

Other than trying to flex mathematical prowess to your examiner there really is not point since it only saves a little bit of time with the possibility of dropping marks.

Some people will say that an assessor have said it's ok but since there is no consensus between everyone it's much safer to just use the table.

How does the sign test actually work?

[S200]

How does the sign test actually work?

If the gradient is positive on one side and negative on the other, it's a maximum/local maximum.

The opposite would be neg - Pos, meaning a minimum/local min.

If it's pos-pos or neg-neg, It's a stationary point of inflexion.

[Bri MT]

I'm pretty sure my teacher was an assessor & we were taught both but better safe than sorry.

As S200 said, pick one point (close by) on each side and see if f'(x) is positive or negative

[S_R_K]

I'm not certain of this, but I think the reason why the second derivative test isn't taught in Methods (although it may be used, as appropriate), is because sometimes it is inconclusive. That is, sometimes the second derivative is zero, even when the stationary point is not a point of inflection. This introduces complications that are fully dealt with in Specialist. So, to avoid these issues, the Methods study design just expects students to classify stationary points using the first derivative test.

In short: you need to know the first derivative test anyway, although the second derivative test can be a useful check / short-cut in some cases.

[sailinginwater]

I'm not certain of this, but I think the reason why the second derivative test isn't taught in Methods (although it may be used, as appropriate), is because sometimes it is inconclusive. That is, sometimes the second derivative is zero, even when the stationary point is not a point of inflection. This introduces complications that are fully dealt with in Specialist. So, to avoid these issues, the Methods study design just expects students to classify stationary points using the first derivative test.

In short: you need to know the first derivative test anyway, although the second derivative test can be a useful check / short-cut in some cases.

First derivative test?

[S_R_K]

First derivative test?

As earlier replies said, checking whether the derivative is positive / negative either side of the stationary point.