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Question No.1tan-1x, |x < 1(x1 – 1), 1x > 1is not differentiable isThe set of pointswhere f (x)(A) {0}(B) {1}(C) {-1}(D) {-1,1}AB.С C​

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113 cents Beverly Wolfe
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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