Find the equation of the tangent line at x = 1
Deriving the implicit function of y with respect to x yields:
but I'm completely stuck on how to find the equation of the tangent line from this (assuming I did this correctly).
This equation doesn't seem to be a function. I get multiple values of y for x equal 1.
Was I tricked?
btw, that implicit function should have read:
Anyway, here's what I got:
Re-evaluating the derivative:
Now substituting y and x
Using the point-slope form
I'd appreciate any comments or criticism on my thought processes or approach, even if the answer isn't wrong.
Ah, thank you.
Substituting for x and y:
Equation of a tangent line in point-slope form
Performing the substitutions:
I'm curious why you said there were two possibilities (1, -1) and (1, 5). Wouldn't that make the dependent value y not a function?