Let f and g be two real valued differentiable function on R such that g ′ ( x ) f ′ ( x ) = f 2 ( x ) g 2 ( x ) ∀ x ∈ R . If f ( 10 ) = 5 , g ( 10 ) = 2 and g ( 2 ) = 1 , then find the value of (

Question

Let f and g be two real valued differentiable function on R such that g ′ ( x ) f ′ ( x ) ​ = f 2 ( x ) g 2 ( x ) ​ ∀ x ∈ R . If f ( 10 ) = 5 , g ( 10 ) = 2 and g ( 2 ) = 1 , then find the value of ( f ( 2 ) ) 3 .

TestHub · Accepted Answer

d x d ​ ( f 3 ( x ) − g 3 ( x ) ) = 3 f 2 ( x ) f ′ ( x ) − 3 g 2 ( x ) g ′ ( x ) = 0 So, f 3 ( 10 ) − g 3 ( 10 ) = f 3 ( 2 ) − g 3 ( 2 ) ⇒ f 3 ( 2 ) = ( 5 ) 3 − ( 2 ) 3 + ( 1 ) 3 = 125 − 8 + 1 = 126 − 8 = 118

Mathematics - Application of Derivative Question with Solution | TestHub

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JEE Main - 1 year (12th class)

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