Find the y -intercept of the curve that passes through the point ( 2 , 1 ) wi

Jay Barrett 2022-05-09 Answered
Find the y-intercept of the curve that passes through the point ( 2 , 1 ) with the slope at ( x , y ) of 9 y 2
d y d x = 9 y 2
y 2 d y = 9 d x
y 3 3 = 9 x + C 1
y 3 = 27 x + C ( C = 3 C 1 )
y = ( 27 x + C ) 1 / 3
1 = ( 27 ( 2 ) + C ) 1 / 3
C = 54
0 = ( 27 x + 54 ) 1 / 3
y i n t e r c e p t = ( 2 , 0 )
Where is mistake?
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Answers (1)

Aibling6n2re
Answered 2022-05-10 Author has 11 answers
You've miscalculated when finding your C . When plugging ( x , y ) = ( 2 , 1 ) into the equation y 3 = 27 x + C (there's no need to solve for y first, since the basic cubic function is invertible), we get
1 = 54 + C ,
Furthermore, you went on to use 54 as your C value, though you allegedly found C = 52. I suspect that at least one typo has been made.
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