Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

4x^2 + xy + 4y^2 = 9, (1, 1) (ellipse)

Answer 1

so, define the derivative for me

Answer 2

in other words, what is giving you an issue with this?

Answer 3

I found y=2-x so is that correct?

Answer 4

4x^2 + xy + 4y^2 = 9

8xx' + (xy)' + 8yy' = 0

8xx' + (x'y+xy') + 8yy' = 0

wrt.x this gives us x'=dx/dx=1

8x + y+xy' + 8yy' = 0, and solve for y'

y'(x+ 8y) = -y-8x

y' = (-y-8x)/(x+ 8y)

y' = -(y+8x)/(x+8y), letting x=1, y=1 from the point

y' = -(1+8)/(1+8) = -1 for a slope

Answer 5

so point slope format is what ...

y = -(x-1)+1 ... so the tangent is y = -x+2

Answer 6

y=2-x is fine :)

Answer 7

Thanks :)

Answer 8

youre welcome