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The function f(x) = |x|+|x - 1| is
  • a)
    Continuous at , but not differentiable at 
  • b)
    Both continuous and differentiable at x = 1
  • c)
    Not continuous x = 1
  • d)
    Not differentiable at x = 1
Correct answer is option 'A,D'. Can you explain this answer?
Verified Answer
The function f(x) = |x|+|x - 1| isa)Continuous at , but not differenti...
Given that f (x) = |x| + |x-1|, then f(1) = 1
Since absolute volue functions are continuous everywhere so f(x) = |x| + |x-1|. being the sum of two continuous function is continuous everywhere. Now we check differentiability at x = 1, we have




Hence Lf'(1) ≠ Rf'(1)
∴ Derivative do not exist at x = 1.
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The function f(x) = |x|+|x - 1| isa)Continuous at , but not differenti...
The answer is A and D
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The function f(x) = |x|+|x - 1| isa)Continuous at , but not differentiable atb)Both continuous and differentiable at x = 1c)Not continuous x = 1d)Not differentiable at x = 1Correct answer is option 'A,D'. Can you explain this answer?
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