Question

How do you find the equation of the tangent line to the curve `f(x)= (x+1)/(x+2)` at x=0?

Answer 1

`y = 1/4x + 1/2`

Explanation:

1) Find the first derivative of f(x).
2) Plug x = 0 into f '(x) to find the slope at x.
3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

1) `1/(x + 2)^2`
2) `1/(0 + 2)^2 = 1/4`
3) `f(0) = (0 + 1)/(0 + 2) = 1/2`
4) `y - 1/2 = 1/4(x - 0)`