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99 Percentile Qs Bank for JEE MainMathematicsContinuity and Differentiability

If f is defined by f(x)= array l x for 0 x < 1 2-x for x 1 array . , then at x=1, f(x) is

Options

  1. Acontinuous and differentiable
  2. Bcontinuous but not differentiable
  3. Cdiscontinuous but differentiable
  4. Dneither continuous nor differentiable

Correct answer

B. continuous but not differentiable

Step-by-step solution

Give function, aligned & f(x)= array lll x & for & 0 x < 1 2-x & for & x 1 array . & At x=1 & f(x)=2-x & f(1)=2-1=1 & LHL = _ x 1⁻ f(x)= _ x 1⁻ x=1 & RHL = _ x 1⁺ f(x)= _ x 1⁺ (2-x)=2-1=1 & LHL = RHL =f(1) & f(x) is continuous at x=1 & To check the differentiability of f(x) , & f^ (x)= array lll 1 & for & 0 x < 1 -1 & for & x 1 array . & LHD = _ x 1⁻ f^ (x)= _ x 1⁻ 1=1 & RHD = _ x 1⁺ f(x)= _ x 1⁺ (-1)=-1 & LHD RHD & aligned f(x) is not differentiable at x=1

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