Let f: R R be defined by f(x)= array ccc + [x] x , & if & x0 2, & if & x=0 + [ x-x x^3 ], & if & x

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Let f: R R be defined by f(x)= array ccc + [x] x , & if & x>0 2, & if & x=0 + [ x-x x^3 ], & if & x < 0 array . equal to

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Correct answer: A. 1 4

Given, f(x)= [e^x ( x-2 x+2 )^ 3 / 4 ] f(x)=x+ 3 4 [ (x-2)- (x+2)] On differentiating w.r.t. x , we get aligned f^ (x) & =1+ 3 4 ( 1 x-2 - 1 x+2 ) & =1+ 3 4 ( 4 x^2-4 )=1+ 3 x^2-4 f^ (0) & =1+ 3 0-4 = 1 4 aligned

Let f: R R be defined by f(x)= array ccc + [x] x , & if & x>0 2, & if & x=0 + [ x-x x^3 ], & if & x < 0 array . equal to

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