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AP EAMCET202422 May 2024Morning ShiftMathematicsContinuity and DifferentiabilityActual

The function f(x)=|x-24| is

Options

  1. Adifferentiable at [0,25]
  2. Bnot continuous at x=24
  3. Cneither continuous nor differentiable on [0,25].
  4. Dcontinuous on [0,25] , but not differentiable on [0,25] .

Correct answer

D. continuous on [0,25] , but not differentiable on [0,25] .

Step-by-step solution

gathered f(x)=|x-24|= array cc -x+24, & x 24 x-24, & x 24 array . _ x 24⁻ f(x)= _ x 24 (-x+24)=0 gathered _ x 24⁺ f(x)= _ x 24 (x-24)=0 and f(24)=0 f is continuous on [ 0,25 ] . Also, _ x 24⁻ f(x)-f(24) x-24 = _ x 24 -x+24+0 x-24 =-1 _ x 24⁺ f(x)-f(24) x-24 = _ x 24 x-24 x-24 =1 f is not differentiable on [0,25] .

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