Question

Let $f:[a,b]\to R$ be a function such that for
$c\epsilon (a,b),f^1\left(c\right)=f^{11}\left(c\right)=f^{111}\left(c\right)=f^{tv}\left(c\right)=f^v\left(c\right)=0$ then

• A. f has local extremum at x=c
• B. f has neither local maximum nor local minimum at x = c
• C. f is necessarily a constant function
• D. It is difficult to say whether (a) or (b)

Answer 1

The correct option is D

It is difficult to say whether (a) or (b)

If even derivative +ive, then minima and if even derivative -ive, then maxima.
But here $f^{vi}\left(c\right)$ is not given.

Hence, it is difficult to say maximum or minimum ie, a or b.