Question

find an equation of the tangent line to the hyperbola y=3/x at the point (3,1) Thanks

Answer 1

dy/dx = slope of tangent line

line goes through point (3,1)
\[\frac{d}{dx} \frac{3}{x} = \frac{d}{dx}3x^{-1} = -3x^{-2} = -\frac{3}{x^{2}}\]
x=3 --> slope = -1/3
\[y-1 = -\frac{1}{3}(x-3)\]
\[y = -\frac{1}{3}x +2\]

Answer 2

thank you :)