point of inflexion (1 Viewer)

[Arithela]

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

 

[dolbinau]

It's the same thing. As far as I know. At least in 2u maths.

 

[hollyy.]

i dont think its the same thing, but i dunno the difference either

 

[tommykins]

回复: Re: point of inflexion

horizontal point of inflextion is when f'x and f''x = 0
point of inflextion is when f''x = 0 but f'x =/= 0

 

[lyounamu]

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

At horizontal point of inflexion, both the first derivative and second derivative are 0.


At point of inflexion, however, the first derivative is not 0 but the 2nd derivative is 0.

 

[Graceofgod]

Hmmmm

Horizontal point of inflexion is where f'(x) = 0 and f"(x) = 0, not just f"(x).

This means that the gradient is 0 at the point, and the concavity changes too. Unlike a normal point of inflexion where just concavity changes.

High five for 2u maths. Don't know why I do it >.<

 

[Arithela]

for this question for e.g.
1)b) Find the coordinates of the point of inflexion.

what happens here?

 

[lyounamu]

for this question for e.g.
1)b) Find the coordinates of the point of inflexion.

what happens here?

How am I meant to find point of inflexion with this limited info?

 

[Arithela]

do we just let f"(x) = 0? what about f'(x)?

 

[12o9]

for this question for e.g.
1)b) Find the coordinates of the point of inflexion.

what happens here?

f''(x) = 0 , remember to show a change in concavity as some schools deduct marks for not showing it

 

[lyounamu]

do we just let f"(x) = 0? what about f'(x)?

Nothing to f'(x).

But if you found that f'(x) and f''(x) both 0 at that point, that's most likely a point of inflexion but you will have to test each side of that point to see that there is no change in gradient.

 

[lepellillow]

also remember when you sketch, that points of inflexion are smooth but horizontal points of inflexion have like a little kink in the curve

 

[Graceofgod]

Normally in a 2u test, the questions like this will give you an equation.

You will then be asked to find the turning points and determine their nature. To do this you find when f'(x) = 0 and then test with f"(x)

If during one of these tests, you get f"(x) = 0, you have found yourself a horizontal point of inflexion.

The next question is usually, as you stated, "Find the co-ordinates of the(any) point(s) of inflexion"

Then the next question is obviously sketch the graph.

 

[locked.on]

do we just let f"(x) = 0? what about f'(x)?

To find a horizontal point of inflexion, you solve for f''(x) = 0 and the root must also be a solution to f'(x) = 0.

 

[lyounamu]

To find a horizontal point of inflexion, you solve for f''(x) = 0 and the root must also be a solution to f'(x) = 0.

No. At horizontal point of inflexion, f'(x) and f''(x) = 0.

 

[Arithela]

ok thanks.. i know how to find pts and nature etc. but horizontal and pts of inflexion confused me. nvm its fine

 

[dolbinau]

Cool. I don't think I was ever taught the difference .

 

[Arithela]

one more question...

does area of major segment = area of sector - area of minor segment?

 

[Graceofgod]

Area of major segment = Area of circle - Area of minor segment by definition

 

[Graceofgod]

When a circle is divided into two segments by a chord, the smaller of the two segments is called the minor segment, the larger the major segment.