What is the tangent of f(x)=(2x)/(x+1),(1,1) ?

The tangent of f(x)=(2x)/(x+1),(1,1) is y= 1/2 x+1/2

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tangent of f(x)=(2x)/(x+1),(1,1)

tangent of

f (x) = \frac{2 x}{x + 1}, (1, 1)

y = \frac{1}{2} x + \frac{1}{2}

Solution steps

Find the slope of

f (x) = \frac{2 x}{x + 1} : \frac{df ( x )}{d x} = \frac{2}{( x + 1 ) ^{2}}

Compute the slope of

f (x) = \frac{2 x}{x + 1}

(1, 1) : m = \frac{1}{2}

Find the line with slope m=

\frac{1}{2}

and passing through

(1, 1) : y = \frac{1}{2} x + \frac{1}{2}

y = \frac{1}{2} x + \frac{1}{2}

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What is the tangent of f(x)=(2x)/(x+1),(1,1) ?
The tangent of f(x)=(2x)/(x+1),(1,1) is y= 1/2 x+1/2