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)
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.
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