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?

Question

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?

Aibling6n2re · Accepted Answer

You&#039;ve miscalculated when finding your   C  . When plugging   (  x  ,  y  )  =  (  2  ,  1  ) into the equation       y    3    =  −  27  x  +  C (there&#039;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.

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

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