A-Level Maths: G3-19 Gradients: Finding Non-Stationary Points of Inflection Example 1

[rafathchowdury]

i dont get why you look at the stationary points when they tell you to find the point of inflection?

[jades]

Best explanation I have seen - thank you so much

[reece]

Can points of inflection also be stationary?

[AceOfHearts]

Nice video!.. Although a lot of working may have been averted if we realised 6x+10 is a continuous linear function with a sign change either side of the root (therefore transitioning from concave to convex).

[Dark-pori]

Would you be able to find the second derivative and set it to 0 and then sub in f(-1.5) and f(-1.7) into the first derivative to show that its going from a positive to positive gradient? or would you need to use the method of showing concave to convex

[riaasx]

Hi Sir, urgent question: Don't we have to check the sign change using dy/dx and not d2y/dx2?

[lukeollerhead]

Great video - Question on this: Is checking a value either side of the (potential) point of inflection, sufficiently rigorous for the exam? I feels like I could conceive of a function where the sign change happens so close to the x-value that this check (an arbitrary distance either side of the x-value) wouldnt work?

[davidoloughlin]

Why do you need to check that the curve goes from convex to concave or vice versa?

[wqltr]

I understand the idea that x= -1.7, -1.6 are close to x=-5/3, and therefore you can check for the sign change. But in fairness isn't this method slightly vulnerable since if there were more roots in d^2y/dx^2 between -1.7 and -5/3 and/or -5/3 and -1.6. I understand that isn't very likely but it makes the method less rigorous.

Also otherwise why not apply this method to showing turning points too? You could plug in points close to a root in dy/dx and show a sign change meaning it is either a minimum or a maximum. But instead you typically take the second derivative?

Could there potentially be a method where you take the third derivative to show a point of inflection?

[senenn]

I thought f''(x) is equal or bigger than 0 means its convex and not just bigger than 0? Thanks

[thomaswinkworth]

I thought that by definition a point of inflection cannot be stationary? Is there an example of such

[harrysmith]

Aren't there points of inflection when f''(x) is undefined aswell?

[jeremypillai]

Hello 
What is the difference between a stationary point of inflection and a non-stationary point of inflection? Thanks