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JEE Main20231 Feb 2023Morning ShiftMathematicsApplication of DerivativesActual

If f x = x 2 + g ' 1 x + g " 2 and g x = f 1 x 2 + x f ' x + f " x , then the value of f 4 - g 4 is equal to _____ .

Correct answer

0

Step-by-step solution

Given: f x = x 2 + g ' 1 x + g " 2 ⇒ f ' x = 2 x + g ' 1 ⇒ f " x = 2 Now, g x = f 1 x 2 + x f ' x + f " x ⇒ g x = f 1 x 2 + x 2 x + g ' 1 + 2 ⇒ g x = f 1 + 2 x 2 + g ' 1 x + 2 ⇒ g ' x = 2 f 1 x + 4 x + g ' 1       . . . . 1 ⇒ g " x = 2 f 1 + 4         . . . 2 Put x = 1 in 1 , then we get 2 f 1 + 4 = 0 ⇒ f 1 = - 2 ∴ g " 2 = 2 f 1 + 4 = 0 Now, f x = x 2 + g ' 1 x + g " 2 Put x = 1 , then we get f 1 = 1 + g ' 1 +

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