Question

Determine the equation of the tangent line to F(x) = (2 - x^2)/(1+x) at (0,2). write your answer in the form Y=mx+b?

Answer 1

y=-3x+2

Explanation:

`y-y_1=m(x-x_1)` is a formula.
m is the slope and its formula like that:
`F^'(x) =m`
So `F'(0) = (2-x^2)/(1+x) = (-1(1+x)-(2-x^2))/(1+x)^2 = (-1-2)/1 = -3`

we know `y_1=2` from the point (0,2)

`y-2=-3(x-0)`
`y-2=-3x`
`y=-3x+2`