Tangent to the curve

**mx-** · April 20th 2008, 04:10 AM

Consider the curve given by $2xy - \sqrt{x^2+y}=-23$ .
Find the equation of the line tangent to the curve at the point (−2, 5)

Thanks

**Mathstud28** · April 20th 2008, 04:25 AM

Originally Posted by mx-

Consider the curve given by $2xy - \sqrt{x^2+y}=-23$ .
Find the equation of the line tangent to the curve at the point (−2, 5)

Thanks

Differentiating implicitly we get $2xy'+2y-\frac{1}{2}(x+2y)^{\frac{-1}{2}}\cdot(2x+y')=0$ now using this we get $y-5=f'(-2,5)(x+2)$ I will leave the evaluation of f'(-2,5) to you...plug it in and solve for y'

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