Find the equation of the tangent line at the given value of x on the curve. 4y^3+xy-y=108x^4; x=1

ucatzABI

ucatzABI

Answered question

2022-11-26

Find the equation of the tangent line at the given value of x on the curve.
4 y 3 + x y y = 108 x 4 ;   x = 1

Answer & Explanation

inventorspotDkt

inventorspotDkt

Beginner2022-11-27Added 5 answers

So when
x = 1 , 4 y 3 + y y = 108 x 4 4 y 3 = 108 y 3 = 108 4 = 27 y = 3
For equation of tangent, differentiate given equation with respect to x
d d x ( 4 y 3 + x y y ) = d d x ( 108 x 4 ) 12 y 2 d y d x + x d y d x + y d x d x d y d x = 432 x 3
put x=1, y=3
12 ( 3 ) 2 d y d x + d y d x + 3 d y d x = 432 108 d y d x + 3 = 432 108 d y d x = 429 d y d x = 429 108
Equation of tangent can be given as
y y 1 = d y d x ( x x 1 )
Here ( x 1 , y 1 ) = ( 1 , 3 )
So, equation of tangent equals to
y 3 = 429 108 ( x 1 ) y = 429 108 ( x 1 ) + 3

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