Is my equation of the tangent line at (2,-1) correct?

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Homework Help Overview

The discussion revolves around finding the equation of the tangent line to the implicit function defined by x^3 - 2x^2y + y^2 = 17 at the point (2, -1). The subject area is calculus, specifically focusing on derivatives and tangent lines.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find the derivative and subsequently the equation of the tangent line. Some participants question the correctness of the derivative and suggest that there may be sign errors and issues with coefficients and exponents.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's attempts. There is a recognition of improvements in the derivative, but further corrections are still needed. No consensus has been reached regarding the final form of the derivative or the tangent line equation.

Contextual Notes

Participants are addressing potential errors in the calculations related to the derivative, indicating a need for careful reevaluation of the expressions involved.

excelsion
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i would like to know if my answer is correct can someone tell me the results for this:
Find the equation of the tangent line to x^3-2x^2y+y^2=17 at (2,-1)

ive gotten y'=(3x^2+4xy)/(-2x^2-y)
and my line equations is
y+1=(-1/4)(x-2)
thanks in advance
 
Last edited:
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I think you have some sign problems in your derivative. Check again.
 
i did it wrong i re did it and got this:
dy/dx=-3x^2+4xy^2/-4x^2+2y

is that correct?
 
The signs have improved, but you have bad exponent in the numerator and a bad coefficient in the denominator. I think if you do it once more carefully, you'll get it.
 

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