1.

Let f:[a,b] to R be a function such that , for c in (a,b), f.(c ) = f..( c) = f...( c) = f.... (c ) = f.....( c) = 0 . Then :

Answer»

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

Solution :`f.(C) = f..(C) = f...(C) = f^(iv)(C) = f^(v) (C) = 0`
Now if n is the least positive integer such that `f^n (C) NE 0`, then it is not clear whether n is even or ODD. So nothing can be said whether `f(x)` has local EXTREMA at x= c or not .


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