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Which of the following function is thrice differentiable at x = 0?

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a
fx=x3
b
fx=x3x
c
fx=xsin3x
d
fx=xtan3x
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detailed solution

Correct option is B

fx=x3=-x3,x<0x3,     x≥0  or   f'''x=-6,  x<06,      x>0Hence,   f''0  does  not  exist.        fx=x3x=-x4,  x<0x4,      x≥0  or  f'''x=-24x,   x<024x,      x>0.Hence,  f'''0=0  and  it  exists.Similarly,   for   fx=xsin3x   and  fx=xtan3x   also,   f'''0=0and   it   exists

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