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KCET2025MathematicsContinuity and Differentiability

The function f(x)= array ll e^x+a x & , x 0 b(x-1)^2 & , x 0 array . is differentiable at x=0 . Then

Options

  1. Aa=1, b=1
  2. Ba=3, b=1
  3. Ca=-3, b=1
  4. Da=3, b=-1

Correct answer

C. a=-3, b=1

Step-by-step solution

f(x)= array cc e^x+a x & , x 0 b(x-1)^2 & , x 0 array . aligned & Continuity LHL =1 & RHL = b b =1 aligned Differentiability LHD =1+ a aligned RHD & =-2 b 1+a & =-2 b a & =-3 aligned

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