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NDA2017MathematicsContinuity and DifferentiabilityActual

A function is defined in (0, ) by f(x)= array ccc 1-x^2 & for & 0 x 1 In & x & for 1 x 2 2-1+0.5 x & for & 2 x array . Which one of the following is correct in respect of the derivative of the function, i.e., f^ ( x ) ?

Options

Af^ (x)=2 x for 0 x 1
Bf^ ( x )=-2 x for 0 x 1
Cf^ (x)=-2 x for 0 x 1
Df^ ( x )=0 for 0 x

Correct answer

C. f^ (x)=-2 x for 0 x 1

Step-by-step solution

f(x)= array l 1-x^2 for 0 x 1 x for 1 x 2 2-1+0.5 x for 2 x array .f^ (x)=-2 x for 0 x 1

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