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.

Question

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.

rogue · Answer

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

rogue · Answer

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

rogue · Answer

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.
$$Y_{tangent} = \frac {1}{4} (x - 1) + \frac {1}{2} = \frac {x}{4} + \frac {1}{4}$$

rogue · Answer

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

anonymous · Answer

yes

anonymous · Answer

thanks

rogue · Answer

Alright, good luck with your studies :)