e^(f(x)) graph (2 Viewers)

[asianese]

Just a question

Why are there inflexion points there and there?

But neither the function nor the exponential have inflexion points??

Also what's the relevance of y=-1?

Thanks

 

[Shadowdude]

I'm pretty sure you differentiated wrong for the second derivative.

 

[asianese]

Oh awks product rule hey?

 

[Shadowdude]

Yep, product rule.

 

[asianese]

So ? *confused*

 

[deswa1]

Forget about the actual derivatives for a second- think about what does -1 or 1 hold when you take something to that power?

 

[RealiseNothing]

edit: nvm i derped hard.

 

[barbernator]

in the HSC they don't mark on the concavity at those points anyway.

EDIT: Actually for that graph they probably would. Just think of what should happen, as f(x) ---> - infinity, e^f(x) = 1/e^infinity so the curve must be approaching 0 with a concavity > 0 .

you don't need to know the location of the inflexion points, just that they must be there because concavity changes

 

[asianese]

Well...

Why does concavity change though???

Marking guidelines

Criteria

- Correct graph (y-intercept not required) 2 marks
- Correct behaviour at x=+/- 1 or correct behaviour as x -> +/- infty 1 mark

 

[barbernator]

Well...

Why does concavity change though???

Marking guidelines

Criteria

- Correct graph (y-intercept not required) 2 marks
- Correct behaviour at x=+/- 1 or correct behaviour as x -> +/- infty 1 mark

well it can't approach 0 while having a negative concavity, it behaves like 1/x as it approaches 0.

And if you double differentiate a function like e^(x^2/x^2-1) it will have an inflection point like that