Question

How do you find the equation of the tangent line to the graph of the given function `f(x) = - 1/x`; at (3,-1/3)?

Answer 1

I found: `y=1/9x-2/3`

Explanation:

First you need to find the slope `m` of the tangent line;
you need to evaluate the derivative of your function:
`f'(x)=1/x^2`
and then evaluate it at `x=3`
`f'(3)=1/9` this will be the slope of the tangent.
Now you can use the relationship:
`y-y_0=m(x-x_0)` that with your values gives:
`y-(-1/3)=1/9(x-3)`
Giving:
`y=1/9x-2/3`