point of inflexion (1 Viewer)

[tradewind]

i don't know how to approach this problem since it asks to give reasons.

give an explanation of what is meant by the term, 'point of inflexion', and give a diagram to illustrate your answer. Also state the condition required for a point to be a point of inflexion.

 

[martin310015]

Point of inflexion is where there is change in concavity.

Take the graph y=x^3 the point of inflexion is at (o,o)

you can use first derivative or the second derivative test.

 

[hatty]

no

point of inflexion is where there IS NOT a change in concavity

how do u find points of inflexion?
find the second derivative
set it to 0
test concavity on each side.
if the concavity is the same,
then it is inflexion point

 

[jesshika]

Originally posted by hatty
if the concavity is the same,
then it is inflexion point

i think yu're wrong there
... a point of inflexion is when there is a change in concavity ..
i.e. the point at which the curve changes from a max to min or vice versa ..
can't be the sameee ... !!
... test each side for the x value that you got when you solved y''=0 .. and if there is a change in concavit then its a point of inflexion ~~

 

[hatty]

0- | 0 | 0+
+ | 0 | +

 

[hatty]

i mite be wrong
ill check up on it

 

[Xayma]

A point of inflexion has a change in concavity, however it doesnt have a change in direction of gradient.

 

[hatty]

yes i just read my maths book and realised my mistake
in my frustration i ripped it out... now i gotta pay for it

oh well, there goes some marks of my half yearly

 

[Heinz]

dont forget about your horizontal points of inflexion

 

[KeypadSDM]

They're no different, it's a change in concavity.

 

[Zarathustra]

What is the difference between a pt of inflexion and an horizontal pt. of inflexion? - apart from the look of them, what ways, other than graphing, can be used to determine whether or not it's an horizontal pt.?

 

[CM_Tutor]

A point of inflexion occurs at any point on a continuous, differentiable curve where concavity changes. It is a horizontal p.o.i. if, in addition to the above, the gradient at the p.o.i. is 0 - These should be determined by examining the behaviour of dy/dx and d²y/dx², not be sketching.