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Numerade Educator

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Problem 34 Medium Difficulty

Find equations of the tangent line and normal line to the given curve at the specified point.

$ y = \frac {2x}{x^2 + 1}, (1,1) $

Answer

Tangent line is $y=1$
Normal line is $x=1$

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Video Transcript

he It's clear. So when you right here, So we have of X is equal to two x over X square plus one. We're gonna difference she using the product quotient rule to get X square plus one D over DX for two x minus two X d over D X for X square plus one all over X square plus one square. This becomes equal to X square plus one times two minus two X tones to X all over X square plus one square, which is equal to two minus two X square over X square plus one square. A slip of detention at one common one become zero, and the equation of change in is why minus one over X minus or unequal. Ciro. So why is equal to one? And we know that the normal line is perpendicular, so it's going to be access equal to one