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

1 Answer
Dec 30, 2016

# 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) #