Third derivative method (1 Viewer)

[buchanan]

Again, your example y=x⁶ is easy by the successive derivative test.

f'(0)=f''(0)=f'''(0)=f''''(0)=f'''''(0)=0 but f''''''(0)=720 > 0 hence (0,0) is a local minimum.

Nevertheless I think the point you are trying to make is what if it's more complicated, like a quotient? The derivatives are more difficult, so even if there is an inflection, and even if the third derivative test works, it probably isn't advisable to use it (or for that matter the successive derivative test either).

For these it's probably easier to just test the sign of f''(x) either side of the point (or points) where f''(x)=0. If it changes sign it's an inflection.

 

[Uncle]

didnt use it, didnt bother using it, never will.
not even in engineering mathematics

 

[arcaox]

regardless of whether it works all the time or not i think the man deserves some sort of praise, his proof was rather interesting but for all your hscers id stick to the normal method that the teachers teach you as you will be required to prove how this 3rd derivative test works if it is true which will consume even more time as it is not in the syllabus and rather a new method you are introducing to the examiner

 

[ninetypercent]

it would be a bitch trying to explain to my retarded teachers how to use the third derivative
and most likely, they will not understand and give me a zero on my exam

so nah.. im not gonna use it

 

[Aquawhite]

I'm going to show this to my teachers and amaze them