anonymous
  • anonymous
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
Mathematics
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
Sorry I mean (-3/4)(x+2) + 3 = y

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anonymous
  • anonymous
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.
anonymous
  • anonymous
Also it is y'y becuase I applied chain rule
anonymous
  • anonymous
got it?
anonymous
  • anonymous
here is an example of implicit differentiation
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