Question

use implicit differentiation to find the equation of the tangent line in the form y=mx+b at the point (-2,3)

x^2+y^2=13

Answer 1

i worked out the whole thing and i came up with y=2/3x+13 but i really don't think i knew how to find my b, but I'm not sure that was my only problem

Answer 2

Alright to solve this take the derivative

2x + y*y' = 0
=
y' = y/2x

now to find the equation of the tangent line we use the formula

f'(x)(x-a)+f(x)

we have the point (-2,3)
so we know f(-2) = 3
and the x value we are looking at is -2
so a = -2

so we have

f'(x)(x+2) + 3

now we need to find f'(-2) and we have our equation of the tangent line to do this
sub in the point into the equation and solve for y'
y' = y/2x
y' = 3/2(-2)
y' = -3/4

we now have f'(-2) = -3/4

so the equation is

-3/4(x+2) + 3 = y

Answer 3

Sorry I mean
(-3/4)(x+2) + 3 = y

Answer 4

the equation I provided is the same as the equation of the line, I have proof but I'm far too lazy to show it.

Answer 5

Also it is y'y becuase I applied chain rule

Answer 6

got it?

Answer 7

here is an example of implicit differentiation