## anonymous 4 years ago hello, may any one help me in this Exercise if (x) =x/x+1 , find f'(x) and the equation of the tangent line to y=f(x) at x=1 , and sketch the graph of y=f(x) and this tangent line.

1. Rogue

$f(x) = \frac {x}{x+1}$By the quotient rule, $f'(x) = \frac {(x+1) \frac {d}{dx} x - x \frac {d}{dx} (x+1)}{(x+1)^2} = \frac {1}{(x+1)^2}$

2. Rogue

The slope of the tangent line at x = 1 is$f'(1) = \frac {1}{(1+1)^2} = \frac {1}{4}$

3. Rogue

f (1) = 0.5 So now we know that the slope of the tangent line is .25 and it passes through (1, 0.5). Plug them into y = mx + b to solve for your b. Then plug in your b & m to get the equation of the tangent line. $Y_{tangent} = \frac {1}{4} (x - 1) + \frac {1}{2} = \frac {x}{4} + \frac {1}{4}$

4. Rogue

Can your graph f(x) and Ytan by yourself?

5. anonymous

yes

6. anonymous

thanks

7. Rogue

Alright, good luck with your studies :)