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If f(x) = |x|, then
  • a)
    f(x) is continuous at 0.
  • b)
    f(x) is not continuous at x = 0.
  • c)
    f(x) is differentiable at x = 0.
  • d)
    None of the above
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If f(x) = |x|, thena)f(x) is continuous at 0.b)f(x) is not continuous...
We have,
f(x) is continuous and differentiable for all x, except zero. We have to check at x = 0.
Left hand limit of f(x) at x → 0,
Right hand limit of f(x) at x → 0,
Value of f(x) at x = 0,
f(x)x = 0 = 0
Thus, f(x) is continuous at x = 0.
Now, check the differentiability.
Left hand derivative:
Right hand derivative:
Since Lf'(x) ≠ Rf'(x), f(x) is not differentiable at x = 0.
Hence, it is not differentiable for all real values of x
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If f(x) = |x|, thena)f(x) is continuous at 0.b)f(x) is not continuous at x = 0.c)f(x) is differentiable at x = 0.d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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