If f x = 1 | x | ; | x | ≥ 1 a x 2 + b ; | x | 1 is differentiable at every point of the domain, then the values of a and b are respectively:

Question

If f x = 1 | x | ; | x | ≥ 1 a x 2 + b ; | x | 1 is differentiable at every point of the domain, then the values of a and b are respectively:, 1 2 , 1 2, 1 2 , - 3 2, 5 2 , - 3 2, - 1 2 , 3 2

MARKS App · Accepted Answer

f x = 1 | x | , | x | ≥ 1 a x 2 + b , | x | 1 at x = 1 function must be continuous So, 1 = a + b … 1 differentiability at x = 1 - 1 x 2 x = 1 = ( 2 · a x ) x = 1 ⇒ - 1 = 2 a ⇒ a = - 1 2 Put in ( 1 ) ⇒ b = 1 + 1 2 = 3 2

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