Q.
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
answer is B.
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Detailed Solution
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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