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Manipal MET2019MathematicsContinuity and Differentiability

If f(x)= array cc x, & 0 x 1 2 x-1, & 1 x array . , then

Options

  1. Af is discontinuous at x=1
  2. Bf is differentiable at x=1
  3. Cf is continuous but not differentiable at x=1
  4. DNone of the above

Correct answer

C. f is continuous but not differentiable at x=1

Step-by-step solution

Given that, f(x)= array cc x, & 0 x 1 2 x-1, & 1 x array . From graph f(x) is continuous, x R . i.e. f^ (x)=1 when 0 x 1 and f^ (x)=2-0 when x 1 . Left hand limit Right hand limit At x=1, f(x) is continuous but not differentiable.

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