Question
Question: Let f : [a, b] → R be a function such that for c ∈ (a, b), f ¢(3) = f ²(3) = f ²¢(3) = f <sup>iv</su...
Let f : [a, b] → R be a function such that for c ∈ (a, b), f ¢(3) = f ²(3) = f ²¢(3) = f iv (3) = f v(3) = 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 (1) or (2)
Answer
f has neither local maximum nor local minimum at x = c
Explanation
Solution
Maxima/minima always occurs at even derivative