x^2y-x=y^3-8 at x=0
Substituting x=0,
So the point of tangency is (0,2), and we want the equation of the
green line below:
We find the slope of the tangent line, which is the
same as the derivative at that point: So we find
the derivative implicitly, i.e., without solving for
the independent variable y:
We substitute x=0 and y=2 and solve for
That's the slope of the tangent line at (0,2), which is
the green line. So
Since the point of tangency is the y-intercept (0,2), we can just
use:
with
Edwin