# Thread: Equation of the Tangent...

1. ## Equation of the Tangent...

If f(x) = 1/x, find f'(3) and use it to find the equation of the tangent to the curve y = 1/x at the point (3, 1/3).

I found the slope to be -1/9 but I don't know how to find the equation

2. You have done
$\displaystyle f(x)= \frac{1}{x}$

$\displaystyle \frac{dy}{dx}= \frac{-1}{x^2}$

And thus got answer $\displaystyle \frac{-1}{9}$

Now equation of a line ,passing through (a,b),with a slope "m" is given by

$\displaystyle (y-b)=m(x-a)$

$\displaystyle (y-\frac{1}{3}) = \frac{-1}{9} (x-3)$