anonymous
  • anonymous
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.
Mathematics
jamiebookeater
  • jamiebookeater
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Rogue
  • Rogue
\[f(x) = \frac {x}{x+1}\]By the quotient rule, \[f'(x) = \frac {(x+1) \frac {d}{dx} x - x \frac {d}{dx} (x+1)}{(x+1)^2} = \frac {1}{(x+1)^2}\]
Rogue
  • Rogue
The slope of the tangent line at x = 1 is\[f'(1) = \frac {1}{(1+1)^2} = \frac {1}{4}\]
Rogue
  • 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. \[Y_{tangent} = \frac {1}{4} (x - 1) + \frac {1}{2} = \frac {x}{4} + \frac {1}{4}\]

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Rogue
  • Rogue
Can your graph f(x) and Ytan by yourself?
anonymous
  • anonymous
yes
anonymous
  • anonymous
thanks
Rogue
  • Rogue
Alright, good luck with your studies :)

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