point of inflexion (1 Viewer)

[joshlols]

Re: 回复: Re: point of inflexion

nah its not e.g. y=x^4 doesn't have one

Thank you captian obvious, because concavity doesn't change.

 

[tommykins]

回复: Re: point of inflexion

Is there ever a case when an x value of F''(x)=0 is not an inflexion point?

i'm assuming f''(x-1) is positive/negative and f''(x+1) is positive/negative respectively.

no change in concavity = a normal point?

 

[dolbinau]

Re: 回复: Re: point of inflexion

Thank you captian obvious, because concavity doesn't change.

His point was you have to test.

 

[danz90]

Re: 回复: Re: point of inflexion

In the Mathematics HSC Exam.. if you are asked to "Find any points of inflexion" for 1 mark... would you also have to test the point or prove its a pt of inflexion, to gain the 1 mark?

 

[Timothy.Siu]

Re: 回复: Re: point of inflexion

In the Mathematics HSC Exam.. if you are asked to "Find any points of inflexion" for 1 mark... would you also have to test the point or prove its a pt of inflexion, to gain the 1 mark?

yes
well, maybe not but how will u know if it is or not? i'm not willing to take a 50% chance for 1 mark (u know wat i mean)

 

[dolbinau]

Re: 回复: Re: point of inflexion

In the Mathematics HSC Exam.. if you are asked to "Find any points of inflexion" for 1 mark... would you also have to test the point or prove its a pt of inflexion, to gain the 1 mark?

In answers for HSC exams I have they always test. It only takes 5 seconds and you could easily just test one side for the concavity then fill the rest in as you know what it will be.

 

[Graceofgod]

Re: 回复: Re: point of inflexion

are you bloody serious?

I think I must have missed some sarcasm or misunderstood your question...

 

[tommykins]

回复: Re: 回复: Re: point of inflexion

I think I must have missed some sarcasm or misunderstood your question...

You're saying since f''[5] < 0 and f''[3] > 0, then f''[4] = 0 which is not true.

What about 4.3? 3.4? 3.2? 4.5678685453 ?

You have to solve the equation for f''[x], you can't simply assume that at x = 4, there is an inflection point.

 

[18836165]

Re: 回复: Re: point of inflexion

In answers for HSC exams I have they always test. It only takes 5 seconds and you could easily just test one side for the concavity then fill the rest in as you know what it will be.

Assuming it is a point of inflexion.

Just simply think about whether it will be positive or negative, don't actually find an exact value unless you can't work it out easily.

 

[mick135]

what is the difference between a point of inflexion and a horizontal point of inflexion? if there is a difference, when do we use them? thanks

I don't know if this is still your question or not - the thread is 4 pages long now. but i can't be bothered reading all 4 pages of gossip so i'm just gonna answer this question.

Definition of Differentiating a function of any kind. Finding the first derivative gives the equation of the "tangent" to the graph - which you sub in particular x and y values to find that particular tangent to each graph.

so a point of inflexion is where the derivative is equal to zero and concavity changes.
ie: F'(X) = 0 or y'=0 (just a stationary point basically)
a horizontal point of inflexion is where the tangent is flat
so when you find the 2nd derivative or F"(X), they = 0

and listen to tommykins = that guy is a brain and a half.

 

[Graceofgod]

Re: 回复: Re: 回复: Re: point of inflexion

You're saying since f''[5] < 0 and f''[3] > 0, then f''[4] = 0 which is not true.

What about 4.3? 3.4? 3.2? 4.5678685453 ?

You have to solve the equation for f''[x], you can't simply assume that at x = 4, there is an inflection point.

Ah good, so it was you who missed what I meant.

We are talking about proving that it is a point of inflexion.

If you find that f"(4) = 0, then check f"(3) and f"(5), you can see if it is actually a point of inflexion.

My question was whether or not you could get away with just saying

f"(3) > 0 and f"(5) < 0 without showing working.

 

[tommykins]

回复: Re: 回复: Re: 回复: Re: point of inflexion

Ah good, so it was you who missed what I meant.

We are talking about proving that it is a point of inflexion.

If you find that f"(4) = 0, then check f"(3) and f"(5), you can see if it is actually a point of inflexion.

My question was whether or not you could get away with just saying

f"(3) > 0 and f"(5) < 0 without showing working.

if that's the case, then yes, you can state f''[3] < 0 and f''[5] > 0 .'. at x = 4 point of inflection as concavity changes.

sorry for the misunderstanding.

 

[Graceofgod]

Re: 回复: Re: 回复: Re: 回复: Re: point of inflexion

if that's the case, then yes, you can state f''[3] < 0 and f''[5] > 0 .'. at x = 4 point of inflection as concavity changes.

sorry for the misunderstanding.

Its cool I got my answer in the end. Thanks.