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

The tangent of f(x)= 2/(x+1),\at x=1 is y=-1/2 x+3/2

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

tangent of

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

y = - \frac{1}{2} x + \frac{3}{2}

Solution steps

Find the tangent point:

(1, 1)

Find the slope of

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

Compute the slope of

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

x = 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{3}{2}

y = - \frac{1}{2} x + \frac{3}{2}

x \to 1 lim (x^{2} - x)

\frac{s ^{2} - 8 s + 15}{s ^{2} + 3 s + 2}

\frac{d}{d x} (\frac{x ^{2}}{4} + y^{2} - 1)

x y^{^{'}} - 2 y = 11 x^{2}

\frac{d y}{d x} = \frac{- y}{x + y}

What is the tangent of f(x)= 2/(x+1),\at x=1 ?
The tangent of f(x)= 2/(x+1),\at x=1 is y=-1/2 x+3/2