Let a curve y = f ( x ) , f ( x ) ≥ 0∀ x ∈ R has property that for every point P on the curve length of subnormal is equal to abscissa of P. If f ( 1 ) = 3 , then f ( 4 ) is equal to

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Given y d x d y ​ = x ; y d y = x d x ; y 2 = x 2 + c ; f ( 1 ) = 3 ⇒ 9 = 1 + c ⇒ c = 8 ⇒ y 2 = x 2 + 8 ; f ( x ) = x 2 + 8 ​ ; f ( 4 ) = 16 + 8 ​ = 2 6 ​ .

Mathematics - Application of Derivative Question with Solution | TestHub

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