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BITSAT2010MathematicsApplication of DerivativesActual

Let ( f ( x )= ) ( array l a x^2+1, x > 1 x+a, x 1 array . ). Then (f(x) ) is derivable at (x=1 ), if

Options

  1. A(a=2 )
  2. B(a=1 )
  3. C(a=0 )
  4. D(a=1 / 2 )

Correct answer

D. (a=1 / 2 )

Step-by-step solution

( aligned & Lf ^ (1)= _ h 0 f(1-h)-f(1) -h & = _ h 0 (1-h+a)-(1+a) -h = _ h 0 -h -h =1 & Rf ^ (1)= _ h 0 f(1+h)-f(1) h & = _ h 0 [a(1+h)^2+1 ]-(1+a) h & = _ h 0 (a h+2 a)=2 a aligned ) Since f' (1) exists, ( L f^ (1)=R f^ (1) a=1 / 2 )

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