Tangent line of a implicit differential equation problem. Question and my wrong answer is in the attached picture

Question

anonymous · Answer

attachment

anonymous · Answer

@mathmate

displayerror · Answer

How did you do the implicit differentiation? I got a different slope.

mathmate · Answer

hint:
from
$x^2+y^2=(3x^2+4y^2-x)^2$...............(1)
we differentiate with respect to x:
$2x+2yy'=(6x+8yy'-1)^2$......................(2)
You would substitute (0,1/4) into .....(2) and solve for y' = slope, and hence find the tangent line passing through (0,1/4).

freckles · Answer

@mathmate are you ignoring the chain rule part of the ( )^2 thing?

freckles · Answer

$$2x+2yy'=2(3x^2+4y^2-x) \cdot (6x+8yy'-1)$$

mathmate · Answer

My bad, forget there was a square to be taken care of!  Thank you!

anonymous · Answer

Did you guys get a slope of 1?

anonymous · Answer

btw sorry for replying late, my internet died last night

anonymous · Answer

Thank you guys for all your help

freckles · Answer

I'm getting that same number.