Question

Find an equation of the tangent line to the curve at the point.

x^2+xy+y^2=7

(2,1)


please show steps! I need to learn how to do it

Answer 1

Have you been taught derivatives

Answer 2

yes, but tomorrow I have an exam on a bunch of stuf and im sooooooo lost!!! I'm just trying to learn it all because I don't understand my professor at all.

Answer 3

okay lets start with this problem. Every time you take the derivative of a y we need to add y'.
Ex) the derivative of 2y^2=6 is 4yy'=0, then you solve for y'

We will do the same above. Let's work one term at a time. What is the derivative of x^2?

Answer 4

2x

Answer 5

Do implicit differentiation in this one i suppose. do it for both y and x

Answer 6

thats the prob idk how

Answer 7

\[-{\frac {x+2\,y}{2\,x+y}}\]

Answer 8

http://www.khanacademy.org/math/calculus/differential-calculus/v/implicit-differentiation this could help

Answer 9

http://www.khanacademy.org/math/calculus/differential-calculus/v/implicit-differentiation--part-2 part 2 is nice too

Answer 10

well when y is dependant variable
-(2*x+y)/(x+2*y)

Answer 11

at 2,1 the slope is
-5
--
4

Answer 12

I figure it out. But, now I'm stuck on the next problem

Answer 13

use
y=mx+b
1=-5/4*2+b

sfb

Answer 14

b=7/2
so

y=-5/4*x+ 7/2 :)

Answer 15

BTW I graphed it and it works fine both the tangent line and the function yyou gave me do you wanna see it?

Answer 16

yeah i already figured it out