If x ≠ 0 and f x satisfies 8 f x + 6 f 1 x = x + 5 , then d d x x 2 f x at x = 1 is

Question

If x ≠ 0 and f x satisfies 8 f x + 6 f 1 x = x + 5 , then d d x x 2 f x at x = 1 is, - 1 14, 25 14, 9 14, 19 14

MARKS App · Accepted Answer

We have, 8 f x + 6 f 1 x = x + 5 ⇒ f - 1 = 2 7 Differentiating on both sides 8 f ' x - 6 x 2 f ' 1 x = 1 Put x = - 1 ⇒ f ' - 1 = 1 2 Now differentiating y = x 2 f x we get, d y d x = 2 x f x + x 2 f ' x at x = - 1 , d y d x = 2 - 1 × 2 7 + - 1 2 1 2 = - 1 14

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