Question

7x^2 + xy + 7y^2 = 15, (1, 1) (ellipse)
find the tangent line at the given point (1,1) by implicit differentiation

Answer 1

Can you do the implicit differentiation part?

Answer 2

I would do
\[ \frac{d}{dx}(7x^2 + xy + 7y^2 = 15) \\
7\frac{d}{dx} x^2 + \frac{d}{dx}(x y) + 7 \frac{d}{dx} y^2 = \frac{d}{dx} 15\]

can you do *any* of those terms?

Answer 3

y=-x+2

Answer 4

correct.