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February 1, 2015

February 1, 2015

Posted by **Nadine** on Monday, December 14, 2009 at 9:03am.

- Calculus -
**MathMate**, Monday, December 14, 2009 at 10:00amUsing implicit differentiation, find the slope of the tangents

y'=x/y

The slopes of the normals are therefore:

y'=-y/x

Rearrange and integrate

∫y'/y = ∫-1/x

ln y = -ln x + C1

ln y = -k ln x

raise to the power of e:

y=C/x

This is the family of reciprocal curves, or rectangular hyperbolas.

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