Question

What is the equation of the line tangent to `f(x)=x^2 + 2/x` at `x=3`?

Answer 1

`y=52/9x-23/3`

Explanation:

For `f(x)=x^2 + 2/x` at `x=3`, we get `y = f(3) = 9+2/3 = 29/3`

The slope of the tangent line is given by `f'(x)`
(I will assume that you know the rules for differentiation. If you need to use the definition and need help, post a comment or another question.)

`f'(x) = 2x-2/x^2`.

So, at the point of interest, the slope of the tangent line is

`m=f'(3)=6-2/9=52/9`.

The equation of the line through `(3, 29/3)` with slope `52/9` is

`y-29/3 = 52/9(x-3)`

Which can be written in slope intercept form: `y=52/9x-23/3`