Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
2x2 + xy + 2y2 = 5, (1, 1)
(ellipse)

Answer 1

\[2x^2+xy+2y^2=5\]
Implicit differentiation yields
\[4x+y+xy'+4y~y'=0\]
Solve for \(y'\).

Answer 2

ok let me try it quick

Answer 3

i got :

Answer 4

Not quite:
\[4x+y+xy'+4y~y'=0\\
y'~(x+4y)=-(4x+y)\\
y'=-\frac{4x+y}{x+4y}\]

Answer 5

my apologies- i see where i made my mistake...would this be my final answer

Answer 6

Nope. \(y'\) gives the slope of the tangent line at any given point. Given the point \((1,1)\), what would \(y'\) be?

Answer 7

so it would be a - 3/5 slope?