A function is defined in 0 infin by f x 1 minus x2 ...........

Mathematics (NDA) Diffrentiation

A function is defined in (0, ∞) by

f(x) = { 1− x² for 0 < x ≤ 1

{ 1nx for 1 < x ≤ 2

{ 1n 2− 1 + 0.5x for 2 < x < ∞

Which one of the following is correct in respect of the derivative of the function, i.e., f′(x)?

f ′^(x) = 2x for 0 < x ≤ 1

f ′^(x) = - 2x for 0 < x ≤ 1

f ′^(x) = - 2x for 0 < x < 1

f ′^(x) = 0 for 0 < x < ∞

f ′^(x) = - 2x for 0 < x ≤ 1 is the right answer.

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