If f(x)+x^2[f(x)]^3=10 and f(1)=2, find f′(1)

Finn Mosley

Finn Mosley

Answered question

2022-11-27

If f ( x ) + x 2 [ f ( x ) ] 3 = 10 and f ( 1 ) = 2, find f ( 1 )

Answer & Explanation

Anabella Moss

Anabella Moss

Beginner2022-11-28Added 9 answers

Start with
f ( x ) + x 2 f ( x ) 3 = 10
Take both sides' derivatives.
f ( x ) + 2 x f ( x ) 3 + x 2 3 f ( x ) 2 f ( x ) = 0.
Set x = 1 in the last equation
f ( 1 ) + 2 f ( 1 ) 3 + 3 f ( 1 ) 2 f ( 1 ) = 0
As f ( 1 ) = 2, we have
f ( 1 ) + 16 + 12 f ( 1 ) = 0 f ( 1 ) = 16 13

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