point of inflexion (1 Viewer)

[wandering17]

When doing the box test, when do you use the first derivative to sub in or the 2nd derivative?

Cause some q's go, that since the concavity didn't change there isn't a point of inflexion, but if there is two positive changes stays the same then isn't it a point of inflexion??

im confused :#

 

[Axio]

When doing the box test, when do you use the first derivative to sub in or the 2nd derivative?

Cause some q's go, that since the concavity didn't change there isn't a point of inflexion, but if there is two positive changes stays the same then isn't it a point of inflexion??

im confused :#

I thought that 'the box method' and 'the second derivative method' were two different methods of determining the nature of stationary points. 'The box method' uses the first derivative and then looks at the slope (+, -, 0).

 

[Lithone]

If you're referring to the box test to determine if a point satisfying f''(x) = 0 is an inflexion point, you need opposite signs on either sides of the point by subbing into 2nd derivative

This shows a change in concavity which is basically the point in making the table

So if it shows +, 0, + (which is what i assume you mean by 2 positive changes) - it's not an inflexion point

 

[dan964]

you can test f'(x) or f'''(x)
you can do what I do which is to draw lines
\ for negative / for positive and - for 0. then you can tell whether it is turning point or not.

 

[braintic]

you can test f'(x) or f'''(x)
you can do what I do which is to draw lines
\ for negative / for positive and - for 0. then you can tell whether it is turning point or not.

I have been assured that HSC markers do not recognise a third derivative test.