use implicit differentiation to find the slope of the tangent line at (3,-2) and use it to find the equation of the tangent line in y=mx + b form

x^3+y^3=y+21

Question

use implicit differentiation to find the slope of the tangent line  at (3,-2) and use it to find the equation of the tangent line in y=mx + b form

x^3+y^3=y+21

experimentx · Answer

use the same technique,

3x^2+3y^2 dy/dx = dy/dx

dy/dx (1-3y) = 3x^2

put the values, find the slope, put all the values on the equation of line also and find b and you have anaswer

experimentx · Answer

Oops sorry here dy/dx (1-3y^2) = 3x^2

anonymous · Answer

ok thats exactly what i got there too but when i put (1-3y^2) under 3x^2 and solve for slope i get -27/11 and then when i solve for b i get 5/11 so my equation is y=-27/11x+5/11  and that is not correct..

anonymous · Answer

y = -27x/11 + 59/11

anonymous · Answer

how did you get the b?

anonymous · Answer

common denominator = 11
27 * 3 = 81 
- 2 * 11 = 22
91 -22 = 59
=> 59/11