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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.
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.

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Rogue
 4 years ago
Best ResponseYou've already chosen the best response.1\[f(x) = \frac {x}{x+1}\]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
 4 years ago
Best ResponseYou've already chosen the best response.1The slope of the tangent line at x = 1 is\[f'(1) = \frac {1}{(1+1)^2} = \frac {1}{4}\]

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.1f (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
 4 years ago
Best ResponseYou've already chosen the best response.1Can your graph f(x) and Ytan by yourself?

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.1Alright, good luck with your studies :)
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