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Consider the function f (x) =  |x| in the interval -1 < x < 1. At the point x = 0, f(x) is
  • a)
    continuous and differentiable.
  • b)
    non-continuous and differentiable.
  • c)
    continuous and non-differentiable.
  • d)
    neither continuous nor differentiable.
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider the function f (x) = |x| in the interval -1<x<1. At the...
Because modulus of X is continuous for all values
But it is not differentiable at x=0 because of sudden change in slope
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Community Answer
Consider the function f (x) = |x| in the interval -1<x<1. At the...
The function f(x) = |x| in the interval -1 < x="" />< 1="" can="" be="" represented="" as="" />

For x < 0,="" f(x)="" />
For x > 0, f(x) = x

So, in the interval -1 < x="" />< 1,="" the="" function="" f(x)="" will="" be="" equal="" to="" x="" for="" x="" /> 0 and will be equal to -x for x < 0.="" />
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Consider the function f (x) = |x| in the interval -1<x<1. At the point x = 0, f(x) isa)continuous and differentiable.b)non-continuous and differentiable.c)continuous and non-differentiable.d)neither continuous nor differentiable.Correct answer is option 'C'. Can you explain this answer?
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Consider the function f (x) = |x| in the interval -1<x<1. At the point x = 0, f(x) isa)continuous and differentiable.b)non-continuous and differentiable.c)continuous and non-differentiable.d)neither continuous nor differentiable.Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the function f (x) = |x| in the interval -1<x<1. At the point x = 0, f(x) isa)continuous and differentiable.b)non-continuous and differentiable.c)continuous and non-differentiable.d)neither continuous nor differentiable.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the function f (x) = |x| in the interval -1<x<1. At the point x = 0, f(x) isa)continuous and differentiable.b)non-continuous and differentiable.c)continuous and non-differentiable.d)neither continuous nor differentiable.Correct answer is option 'C'. Can you explain this answer?.
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