Applications Of Derivatives Question 73
Question: Let $ f:[a,b]\to R $ be a function such that for $ c\in (a,b),f’(c)=f’(c)=f’’’(c)=f^{iv}(c)=f^{v}(c)=0 $ . Then
Options:
A) f has a local extremum at x = c
B) f has neither local maximum nor minimum at x = c
C) f is necessarily a constant function
D) it is difficult to say whether or (b)
Show Answer
Answer:
Correct Answer: D
Solution:
[d] For $ f(x)=x^{6} $ and $ f(x)=x^{7},f’(0)=f’’(0)=f’’’(0) $
$ =f^{iv}(0)=f^{v}(0)=0 $ . $ x=0 $ is point of minima for $ f(x)=x^{6} $ . But $ x=0 $ is not point of maxima/minima for $ f(x)=x^{7} $ .
Hence, it is difficult to say anything.
BETA
