Mathematics

Mathematics

Problem

Let

f'(x)=|x-1|

for all real

x

, and suppose

f

is twice differentiable wherever possible. Which of the following statements about

f''

is correct? a)

f''(x)=0

for

x\neq1

, and

f''(1)

does not exist b)

f''(x)

does not exist for any real

x

c)

f''(x)=-1

for

x<1

,

f''(x)=1

for

x>1

, and

f''(1)

does not exist d)

f''(x)=1

for

x<1

,

f''(x)=-1

for

x>1

, and

f''(1)

does not exist

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