Limit Continuity and Differentiability 7 Question 16

16. Let f(x)=||x|1|, then points where, f(x) is not differentiable is/are

(a) 0,±1

(b) \pm 1

(c) 0

(d) 1

(2005,2M)

Show Answer

Answer:

Correct Answer: 16. (a)

Solution:

  1. Let, g(x)=f(x)x2

g(x) has atleast 3 real roots which are x=1,2,3

[by mean value theorem]

g(x) has atleast 2 real roots in x(1,3)

g(x) has atleast 1 real roots in x(1,3)

f(x)21=0. for atleast 1 real root in x(1,3)

f(x)=2, for atleast one root in x(1,3)



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