Question

Find the slope of the tangent line to the ellipse given by x2 + 4y2 = 4 at the point (√2, -1/√2)

Answer 1

implicit differentiation

Answer 2

\[2x+8y \frac{dy}{dx}=0\]

Answer 3

\[8y \frac{dy}{dx}=-2x\]

Answer 4

\[\frac{dy}{dx}=\frac{-2x}{8y}\]

Answer 5

reduce and substitute x and y into derivative to get slope

Answer 6

but when using the long way, it came out to be -1/2 and the answer should be 1/2 when using implicit differentiation

Answer 7

save this it will help you a lot http://www.wolframalpha.com/

Answer 8

I got -1/2 through implicit... make sure you subtract 2x from both sides to get the negative.

Answer 9

http://www.wolframalpha.com/input/?i=x2+%2B+4y2+%3D+4

Answer 10

oops

Answer 11

see

Answer 12

yeah, I got 1/2

Answer 13

negative from derivative and negative in the y term make positive

Answer 14

did that help you any

Answer 15

???

Answer 16

that is implicit differentiation, but when i do it in the other way, it came out to be an opposite sign answer