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Answer:

We have f(x)=

1+∣x∣

x

;x∈R

⇒f(x)={

1+x

x

;x≥0

1−x

x

;x≤0}

To check for differentiability of the above function we start off by checking for differentiability of f(x) at x=0 since the functional definition is altered at x=0. So let's find the right hand derivative (RHD) and left hand derivative (LHD) at x=0

RHD :

lim

x→0

+

x−0

f(x)−f(0)

lim

x→0

+

⎝

⎜

⎜

⎛

x

1+x

x

−

1+0

0

⎠

⎟

⎟

⎞

=

63

Beverly Wolfe

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