Can you please help me with my calculus test corrections? Please ignore my work and provide a clear solution to each of the questions. Thank you so much!

12.) Consider the curve defined by 213 + 6x2 y -12x2 + 6y=1 a.) Find dy =. dx 6 4. 4 + j (6x)+ 1230(4 )-24x+ 69 6 jy + y ( 62 ) + ( 12 x4 - 24 x+ 6y' = 0 6 y y x ( 6 4 + 6 x 2 ) = - 1274+ 24 2 6 4 + 62 y = = 12 x4 + 24 x 642+ 6x2 b.) Write an equation of each horizontal tangent line to the curve. - 1 2 x4+ 24x = 0 25 ( - 124 + 24 ) = 0 -3 - 12 4 + 24 = Q 2 4 - 2 - 124 2 - 2 4 = 2 c.) The line through the origin with slope -1 is tangent to the curve at point P. Find the x- and y-coordinate of point P. X = 0 -3 4 = O