Finding Horizontal Pt of Inflexion (1 Viewer)

mreditor16

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Hi Guys,

Revising for a quiz soon, and got stuck on this one as well! Any help will be greatly appreciated!! :)

 

InteGrand

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Hi Guys,

Revising for a quiz soon, and got stuck on this one as well! Any help will be greatly appreciated!! :)








For horizontal points of inflection, we want the following to be satisfied:





.

Now we can see where Equations (1) and (2) take us in terms of getting suitable values of x and a, and we just need to make sure we reject any solutions that would make the third derivative 0.
 

InteGrand

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The list of equalities does not need to stop at the second derivative, it just needs to stop at an even derivative and the next one (an odd one) must be non-zero.
 

integral95

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For horizontal points of inflection, we want the following to be satisfied:





.

Now we can see where Equations (1) and (2) take us in terms of getting suitable values of x and a, and we just need to make sure we reject any solutions that would make the third derivative 0.
He wouldn't have learnt that property yet.

He would only need equations (1) and (2) that you've mentioned


In (1) you find x in terms of a and sub into (2) and solve from there.
 

InteGrand

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He wouldn't have learnt that property yet.

He would only need equations (1) and (2) that you've mentioned


In (1) you find x in terms of a and sub into (2) and solve from there.
The problem is, Equations (1) and (2) alone wouldn't generally guarantee that it's an inflection point. We'd need to at least test our values of a and x in some way (e.g. with table of values) to show that it's not a local extremum.
 

photastic

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Is this question any different to high school?
 

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