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

The tangent of f(x)= x/(x+1),\at x=1 is y= 1/4 x+1/4

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

tangent of

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

y = \frac{1}{4} x + \frac{1}{4}

Solution steps

Find the tangent point:

(1, \frac{1}{2})

Find the slope of

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

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{1}{4}

Find the line with slope m=

\frac{1}{4}

and passing through

(1, \frac{1}{2}) : y = \frac{1}{4} x + \frac{1}{4}

y = \frac{1}{4} x + \frac{1}{4}

\frac{d}{d x} (2 x^{2} y)

(x^{2} - x) \cdot e^{- x}

\int \frac{2 x + 4}{x ^{3} - 2 x ^{2}} d x

\int π cos (n x) d x

\int_{0}^{1} 6 e^{- 6 x} d x

What is the tangent of f(x)= x/(x+1),\at x=1 ?
The tangent of f(x)= x/(x+1),\at x=1 is y= 1/4 x+1/4