Question

Use implicit differentiation to find the slope of the tangent line to the curve y/(x-2y) = y^3 +9 (1,10/21)

ive done this problem around 10 times and i still cant get it....
when i did it the last time i got -9-y^3/ 3y^2 x - 8y^3 - 19
and the slope around 0.4754 but it is still wrong i don't know what i am doing wrong..

Answer 1

First off, plug in (1,10/21) and see that it is not a solution to the equation.

Do you mean

y/(x-2y) = x^3 +9 ?

(1,10/21) is a solution to that